"...distinguishing between the perception of the deepest reality, and the mere illusion of such a perception. How can the two be distinguished?"

This is an excellent point. It is one that has been discussed by various gurus over the centuries. And it segues into a topic that would be interesting for you to cover, which is how a person can be swayed into belief that is, to most others, absurd. I would include religious teachings in this absurdity, at least when the teachings are taken literally. I would also include the idea of a flat earth, the outright condemnation of science, and political extremism. This topic was covered, but not very well, by Michael Schermer in his book about belief, as well as a book I read a long time ago by Eric Hoffer called The True Believer. As you know, people can be deluded or confuse or conflate one thing for another. The cause, to me at least, is quite clear, but it's the most persistent psychological pandemic in history.

So back to your question of distinguishing between the perception of the deepest reality...

First, to the outside, which is to say someone who is not involved in the perception but rather hearing about it and trying to assess it or make sense of it based on their own pool of knowledge, feelings, experiences, judgments, etc., there is no way to distinguish at all. He would have to have had the perception himself to recognize what the perceiver is talking about.

Second, for the one who is having the perception... This is difficult to describe and I can only attempt to give an answer based upon my own perception. There must be an understanding of one's own mind and how it works by observing it closely — usually for many years — and recognizing when it is analyzing versus being completely clear and without thought; when it is existent and when it is not; when there is meaning and when there is not. Such clarity is without intent and in the state of the deepest reality there is nothing at all that can be called "something," some thing that is fundamental. There is a complete stillness that seems to be behind, beneath, or prior to, all movement and phenomena. And this stillness is one's "true Self." This is a spatial metaphor not to be taken literally, because there really is no front, back, behind, etc. There is also no sense of a me or doer and there is no split between the seer and the seen.

At the deepest point there is nothing at all gong on, which is complete absence of anything, not only of the sense of self but everything else, including the environment. As I have mentioned, there is no describing any of this while in its depths. It is only afterward that the mind tries to cobble together what has been realized. What remains, however, is a realization that the sense of self is not what one is, nor is any phenomenon, memory, identity, etc.

It seems to my realization that many people have had the experience of annihilation of the self, but upon return, so to speak, they continue to identify as a body and person relating to an objective world, but I am talking about realizing that there is nothing that is not you as the essence of some sort of fundamental, baseline space or essence.

The ultimate perception, then, is the full realization that one is this space despite whether the body and the world appears or disappears. Are you in the world or is the world in you? Can you see past the superficial forms, expressions and bodies to know that all is one movement in consciousness?

I speak of a humbling perception, because there is no one to boast about it or start lecturing to others what they really are or what they should believe. And when you find this you perceive life to be a sort of play, like a dream, where everyone and everything, is a product of your own mind and there is nothing external to it.

The idea of "the other" becomes extinguished.

To answer your question, when there is an illusion of this perception, in which I would include an intellectual or perhaps academic understanding, then the "other" is ever-present and one relates to the actor in the play of life instead of the essence that is in every aspect of the play and without a locus.