I see this, although by different terms. The reptilian brain, as I recall, deals with survival; heart rate, breathing, etc. The sub- (or un-) conscious mind dealing with instinct, and the conscious mind in humans dealing with thought.
This is a different way of parsing the brain, into its major constituent suborgans. The medulla oblongata or "brainstem" is what controls heart rate, breathing, and other "autonomic" functions. The cerebellum is what stores "programs" of sequential co-ordinated muscle movements that we do not have to think about: for example, we think about "walking" across the room and not "raise left foot, move it forward, lean a little bit so I don't fall over, now put it down" as a baby first learning it has to do; or more extremely, I may get in the car and suddenly "find myself" at work, although I meant to go to the grocery store, because I was not thinking about what I was doing and the "program" kicked in. In humans, the cerebellum starts out fairly blank: a horse by contrast knows how to stand and walk (at least a little) from birth; these inborn programs are what are called the "instinctual" behaviors.
The cerebrum is the more complex information-processing organ; sometimes the cerebrum and cerebellum are grouped together as the "forebrain" as opposed to the "hindbrain" (medulla, and its immediate attachments) and the "midbrain". The midbrain suborgans are numerous, thalamus, hypothalamus, amygdala etc. and rather difficult to characterize in simple terms because of the multiple connections and ways of functioning. For example the hypothalamus acts directly on the pituitary, but the hypothalamus is electrical while the pituitary is strictly chemical, issuing "control hormones" that direct the release of other hormones by glands all over the body, so the pituitary is not considered "part of the brain" although it is surrounded by the brain. The pineal is very hard to classify: it acts chemically to set the "body clock" by rising and falling levels of melatonin (not to be confused with melanin, the brown skin-prigment) over the course of the perceived day-night cycle, which it resets based on electrical signals from the visual cortex in the cerebrum (in many reptiles, the pineal is on the surface with its own visual receptors, a "third eye" but one that perceives only light/dark without image-processing); and the pineal also acts chemically on the electrical systems through the "neurotransmitter" chemicals (serotonin, dopamine, etc.) that govern the rate of propagation and suppression of various kinds of electrical signals.
The threefold distinction among hindbrain, midbrain, and forebrain is not what I meant by "Snake/Doggy/Monkey". The reptilian brain does include "midbrain" and "forebrain" organs although the cerebrum is not very large (it processes the pressure senses, feeling/hearing, and also has a visual cortex; the olfactory senses, smell/taste, are processed in a separate vomeronasal organ, vestigial in us); to what extent the Komod dragon is "conscious" I could not say (I suspect that, actually, the question is itself ill-formed). But the Komodo dragon does not feel "sorry" for the dragon hatchlings it eats because it has no emotional circuitry at all, and does not have the ability to model the hatchlings as "other dragons like me", perceiving them only as "tasty snacks". What the mammalian brain adds, besides an enlarged cerebrum integrating all the senses, is a "limbic" network with all kinds of mysterious feedbacks between the forebrain and midbrain organs; somehow this governs emotion (even if I was expert in neurology, I could not explain because the experts themselves is just starting to grope). The crucial functioning here is the ability to construct an internal model of another mind and imagine how the other will respond.
What the "Monkey" adds is a great expansion of the cerebral cortex, with novel connectivity in "Broca's region" and "Wernicke's region", whose functions are even more difficult to unravel than the limbic system, but damage to those areas result in aphasia (loss of language ability) or lesser linguistic malfunctions like dyslexia. Abstraction, and meta-abstraction, are the functionalities here.
I suppose it is possible, if these are all a part of human make-up (I do question beauty/chaos), that we might be subject to any one of them (or more) at a given point in time.
We are subject to all of them, at all points of time, to various degrees. The later-acquired sections of the mind do not kick in until later in life: we are all born as "Snakes", incapable of perceiving anybody beyond ourselves, or putting importance on anything beyond immediate pleasure and pain. We become socialized into "Doggies" who go along with what the pack tells us to do. Eventually, usually in our teens, our "Monkey" becomes dissatisfied with thinking only at that level.
"Kohlberg" is a name you should Google; he had a theory of "stages of moral development" (at its most basic, with three stages based "reward/punishment", "social approval/disapproval", "universal principles"; divided into six or more substages in his more refined papers) which has given rise to a huge body of literature, especially as it relates to the classifying of the differing ethical systems we find in various cultures and religions. Fundamentalist Christianity is a classic "Doggy" system: the pack-leader tells you what to do; the "Snake" is to be kept chained up, and the "Monkey" is blindfolded. Arguments between atheists and fundamentalists often end up talking past each other: the fundamentalist accuses the atheist of wanting to loose the Snake, when the atheist really wants to open the Monkey's eyes.