Descartes was right, consciousness is fundamentally subjective, in a way entirely contrary to objective physics.
From the perspective of physics, consciousness violates this rule: [walks like a duck, quacks like a duck, is a duck]. Two consciousnesses which appear objectively identical can and will behave differently, because of inaccessible internal properties. This is what's called [free will] though, refresher: both determinism and libertarianism are in fact identical propositions, which means they're probably both the same false proposition.
With a physical clock, you can bust it open and look at how the gears are related to each other, and derive its behaviour from its component parts.
Subjectivity is unitary, due to the nature of subjective epistemology. It has no component parts, but is instead one single whole. Though it does have a varying texture which sometimes simulates sub-components.
You can access a separate clock. Your body is a machine, the clock is a machine; you can relate machine to machine. To access the internals of a mind is to violate laws of subjective epistemology. To access a separate mind, you must become that mind, meaning it is no longer separate and [access] is not the correct term for the relationship. Two must become one (if that's possible). You cannot relate mind to mind, because in the case of direct mind-mind contact, it is all one mind which is merely thinking about itself.
You can take a gear out of a clock and it's still a gear. You can't take a thought out of a mind without mutilating the mind, changing both thought and mind, meaning what you took out of the mind wasn't the thought you want to look at. There is no dismantling, nor reassembly. There is only destruction or unification. That said you can make a similar thought in your own mind - assuming you already have a mind to think with, unlike e.g. a silicon computer. This is like examining a clock by building a whole new clock and tweaking it until it works the same way as the old clock.
Consciousness still isn't supernatural. It obeys logical positivism. Although the physical components making up the consciousnesses may be identical, you can still investigate the internal properties of the minds by watching their behaviour and extrapolating inward. Caveat: again this is only possible if you have your own mind with which to make an analogy. You can think thoughts until you run into the thought that would cause the observed action, then conclude that thought was the driving property.
The possibility space, from a physical perspective, is literally infinite. Not only must you list every possible thought, you must list of every possible way for thoughts to interact with each other. Not mere combinatorial explosion: literally infinite. No amount of evidence can narrow it down sufficiently; the prior probability of any hypothesis is literally 0%, and stays 0% eternally because no matter how many you rule out, there's still infinity other possibilities left, all sharing the same finite probability pool. However, the fundamental nature of conscious existence is immediately apparent from the inside of consciousness, again due to the inherent nature of subjectivity. This tells you which things contradict the nature of consciousness, which narrows the possibility space to a finite value.
P.S. Similar to the way libertarianism and determinism are in fact the same: since morality isn't real, virtue ethics, deontological ethics, and consequentialist ethics are in fact the same, identical thing. Nothing = nothing = nothing. Since their foundation is nothingness, their illusions, to even appear consistent, must all be consistent with nothingness. All three illusion are founded on the same error/lie, altering nothingness to appear somethingy in the same way, so even the illusions are perfectly identical.