(These are just my thoughts, not an official representation of any authority on the matter. Some of the terms presented here use my own idiosyncratic definitions and may have different meanings elsewhere. It's also not at all a comprehensive view on the topic but only a rough summary based on my limited understanding.)   I've spent the past year or so really trying to wrap my head around the essence of Tier 2 cognition (starting at Yellow), namely systems thinking. Just these past 6 months, after taking some courses in communication theory and community psychology, I've gotten some insights into the matter that really solidified my previous intuitions which I'd like to share here. I was truly surprised of how much these two fields were based on systems theory (mainly the theories of Gregory Bateson and Urie Bronfenbrenner respectively, although these two theorists only serve as lightning rods for the vast meta-theoretical space that is systems thinking).

I'll open up with a quote from each of the aforementioned theorists:
What these quotes have in common is that they emphasize relationships or interconnections. That is what a system is: a collection of relationships. But isn't it the case that anybody can understand concepts such as "relationships", "interconnections" and "systems"? What makes systems thinking so special? Now, you could actually argue that systems thinking itself isn't necessarily confined to Tier 2. However, I'll say that Tier 2 cognition consists of something called a "mature systems view." It's about a way to view the world; a worldview, and it's of a certain sophistication or maturity. To truly understand this worldview, we must first contrast it with a more common worldview, which I will call "analytical thinking."   Analytical thinking

Fritjof Capra, a pillar of the mature systems view, refers to this worldview and way of thinking as the "Cartesian-Newtonian paradigm." It's characterized by reductionism, mechanism, atomism and positivism. The Cartesian method approaches understanding the world by breaking it down into smaller components (reductionism). Newtonian mechanics describes the world as force interactions between physical objects that consist of atoms (mechanism, atomism). Positivism refers to the idea that we can formulate consistent laws based on this type of knowledge (e.g. "laws of physics").

Another way to think about it is that analytical thinking approaches the world "vertically":

This vertical approach isn't just confined to the hard sciences (physics, chemistry, biology). It's also central to fields like psychology. The analytical tradition of psychology reduces problems down to components within the individual: symptoms, diagnoses, traits, drives, genes, beliefs, values etc. It lays the basis for individual psychotherapy (psychoanalysis, Cognitive Behavioral Therapy etc.), psychiatric medical treatment (antidepressants, anxiolytics etc.), personality psychology (Big 5, MBTI etc.), cognitive psychology (e.g. Beck's schema theory) etc. Jordan Peterson is a big proponent of this view.

On the other hand, there is a systemic tradition within psychology called community psychology. It emphasizes relationships, connections and environmental factors when solving problems (social, economic, political, cultural etc.). Not coincidentally, Jordan Peterson is not a big fan of this approach. Without making this any more about our beloved JP, let's get straight to it: what is systems thinking?   Systems thinking

In contrast to reductionism, mechanism, atomism and positivism, systems thinking is relational, holistic, ecological and organic. 

A system is a collection of relationships between units, and holism is about focusing on the whole. Taking a systems view is about seeing the interplay as a whole, not just the individual units for themselves. The bigger the system view, the greater and more inclusive the whole becomes, and the more holistic it becomes. Ecology is about understanding the relationships between organisms and their environment, and an organism is an interplay of smaller living units ("organs" or organic units). Systems in nature and society are complex and can be described using different concepts from systems theory (e.g. "transaction", "self-organization", "adaptation", "feedback" etc.).

In contrast to the vertical nature of analytical thinking, systems thinking is "horizontal":   This picture represents a social system, however the horizontal principle applies to other systems as well: organ systems, cells, molecules, atoms etc.). These are «real systems» (natural/social systems). You also have abstract systems (e.g. scientific theories, ideologies, value systems, meta-systems, paradigms, meta-theories etc.), and that's where things like construct awareness come into play (more on that later).

Meta-theories are "theories about theories", which try to understand how abstract systems work through meta-systematic observations. Fields like philosophy of science and models like Spiral Dynamics and Integral theory are examples of such meta-theories. Model of hierarchical complexity (MHC) is a good model to understand the different levels of abstract systems (e.g. "how complex is a paradigm?").   Context awareness, Construct awareness and Theory pluralism. I've already mentioned construct awareness, which is one of three main facets that I think are useful to further understand systems thinking:   Context awareness refers to the general ability to understand the pervasive nature of relationships in the world: the vast array of relationships across different domains (physical, biological, social etc.). Any individual unit exists within a larger context (their environment or the larger system), and being aware of context is synonymous with a general form of system awareness.

Bronfenbrenner's Ecological systems theory is a good illustration of context awareness:   Construct awareness is the ability to the understand the relationship between the human and the world with respect to making sense of the world (knowledge, sensemaking and epistemology) and how it's a process of constructing abstract systems. People may manipulate these abstract systems without understanding how they work, e.g. what kind of system it is, how it's made, and how it relates to other systems, which would be an exercise in construct blindness. For example, it's possible to operate a car without knowing how it was made or how the engine works. To not be aware of how abstract systems work to construct your reality is to have a lack of construct awareness.

Thomas Kuhn and his book "The Structure of Scientific Revolutions" is a good example of construct awareness. After performing a meta-theoretical study on the historical development of science, he concluded that all scientific theories at all times are validated relative to a historically contingent framework of philosophical assumptions (a paradigm, a collection of constructs), and thus all scientific knowledge is fundamentally relational in nature. So not only are the external aspects of human behavior dependent on context (as in social interactions; Bronfenbrenner), but also the internal aspects (mind). If we go back to Gregory Bateson, in his systemic communication theory, he in fact defines "context" not as something external, but as an internal psychological framework. He does this because of the insight that the mind is constructing the external world. Alfred Korzybski's "the map is not the territory" is also a staple of construct awareness.
  With enough context and construct awareness, you'll inevitably end up with theory pluralism: the ability to explore and understand a wide range of different abstract systems (theoretical frameworks). In a sense, theory pluralism is both a prerequisite and a consequence of construct awareness (they're co-created). However, to really develop a wide knowledge of theory, you must have a deep meta-theoretical understanding which is able to see the larger picture – the essence of construct awareness. Ken Wilber is a great ambassador for theory pluralism. His vision of integrating all domains of knowledge into a single, comprehensive framework is the pinnacle of systems thinking. Fritjof Capra should also be mentioned here with his book "the Tao of Physics", where he not only makes profound observations about context and construct in his writings about Quantum Mechanics, but he also makes theoretical comparisons to Taoism and non-duality.
  I mentioned earlier regarding having a "mature systems view" that systems thinking is not necessarily confined to Tier 2 cognition. This is because Green is very open to context awareness and will easily appreciate models like Bronfenbrenner's ecological systems theory. What Green struggles with the most is construct awareness. It might be able to deconstruct a lot of Orange systems, both from a rational place and an intuitive place, but it struggles to pick up the pieces, both theoretically and practically. Construct awareness also makes you more prone to grasping the concepts in systems theory, which unlocks key concepts like the meta-theoretical evolutionary lens (Beck & Cowan, Wilber, Kuhn), which Green crucially lacks.
  So that is the gist of it, but there is so much more I could talk about, e.g. the history of systems theory (deep ecology, cybernetics, Gestalt psychology etc.) and different systems theory concepts like I've alluded to earlier. There are also other aspects of Tier 2 cognition that could be expanded upon, like the ability to hold paradox, understanding holarchies, or different real-life applications (that's a big one). I would anyways like to hear what you guys have discovered about systems thinking that I've left out. I would never turn down the opportunity to deepen my theory pluralism                           Additional notes and clarifications: Expanding on this:   Analytical thinking and systems thinking must not be thought of as diametrical opposites, but as generally expressing different dimensions of movement through abstract systems (vertical vs. horizontal). Neither of them are pure expressions of either "vertical" or "horizontal" thinking, because technically all abstract thought utilizes both dimensions to navigate the cognitive landscape. An alternative description could be hierarchical movement vs. cross-hierarchical movement. The categories explored in hierarchical movement tend to have a corresponding familiarity or similarity of kind, while the ones in cross-hierarchical movement have corresponding distance or diversity of kind (in that it's possible to have many qualitatively very different things interacting with each other in a system).
  One reason why horizontal movement tends to be more readily associated with complexity might be due to the relative simplicity of postulating it abstractly, because meanwhile it's possible to have interactions between many qualitatively different things, it doesn't actually necessitate or force a qualitative difference (e.g. you can simply have interactions between many molecules of the same kind), meanwhile a comparably complex vertical scenario is much harder to postulate, as the different levels of a hierarchy always forces a degree of difference (e.g. molecule > atom > sub-atomic), and thus most abstract hierarchies tend to be simpler (because models are supposed to simplify). In other words, the tendency towards horizontal complexity could simply be a bias of abstraction, and that in reality, systems are equally infinitely complex across all dimensions, both vertically and horizontally. Thinking is nevertheless about abstraction, and therefore horizontal thinking serves as a litmus test for complex thinking.   So from this alternative view, what is systems thinking? Well, the more you refine your general ability to abstract both vertically and horizontally across categories (symbols, concepts, classes and domains), the more expansive and complex your thinking becomes. Therefore, the proclivity towards the mature systems view simply depends on the size and complexity of one's perspective. Horizontal thinking is nevertheless generally an indicator of complex thinking.