So I think I was awake all night trying to prove that “The Self” exists 
- so I’m definitely exhausted. But here is what I have so far, at least for a basic understanding of my thoughts. I based the concept on this philosophical line of reasoning; Can The Chariot Take Us To The Land of No-Self.
My version follows some of my definitions, which I will try to define for their context. The basic premise is thus;
A Real, an existent entity; in this case the person, is a Whole; a unified entity, a unified whole; a unity.
The Whole, or Real is not:
a. One of its proper parts. A mere individual piece or pieces of itself, or experiences.
b. The mere sum of its proper parts. The mere sum of its pieces, or experiences.
c. Something wholly distinct from its pieces, or experiences.
D. Reduced to any one of, or sum of; a and/or b (and/or c).
*The Whole, or Real; is more than a piece or sum of its parts, or experiences.
The Whole, or Real; has capacity (is existent, especially) is aware (conscious), is self-aware (self-conscious).
The Whole, or Real; is transcendent of its pieces or sum; its experiences, and simultaneously immanent in them.*
Now that we’ve set a few ground definitions, or concepts, let us proceed. The Real I propose is the person, the “I”, the trueself that is aware and self-aware; that is conscious, and has conscious experiences of “conscious states” and the transition(s) between those conscious states. The Real is aware of states, and aware of transitions between states of consciousness, or conscious experience. As the article I linked states; it is aware of the state of pleasure, and the state of pain, and directly experiences; is aware of, the transition between the state of pleasure and pain.
The Real in essence has conscious awareness of a continuum of conscious experiences; states and transitions. Yet it is not reduced or reducible to any experience, or part, of this continuum. Neither is it reduced or reducible to the mere sum of the continuum. The Whole or Real transcends the continuum in not being reducible to it, yet it is still immanent within the continuum it experiences; and so the continuum is part of the Whole and the Whole is part of it in experiencing the continuum intimately, and thereby that continuum becomes part of the “reality of the Real” - part of its unique history, and thereby part of its its unique perspective.
The Whole, The Real, by its transcendent awareness of its experiences, unifies those experiences; unifies the conscious states, and transitions into a related continuum - which becomes unified into the experience of the Real, and so becomes part of the Real’s reality. The Real is a person, a self, by virtue of its unique perspective and history; by being that real as opposed to that other Real, though all “reals” are one via The Reality, or put another way; all existent entities are one with one another by the virtue that they exist via Existence.
The Real’s transcendent consciousness must be an enduring consciousness. It must be enduring by virtue of the fact that it must be aware of the change, the transition, between conscious state to conscious state; from experience to experience. If there is no enduring consciousness there is no retention of awareness from state to state. If there is no unifying, enduring, transcendent consciousness, there is no unification of conscious experiences within which the Real is simultaneously immanent. The Real would be only aware of one immediate snapshot of conscious state, the immediate present, and would not retain any awareness of the continuum, such as memory or knowledge of it, or any conscious state within it except the immediate present, having ever occurred. The consciousness, the awareness of the Real would be dysfunctional, and limited solely to the immediate present; and if, as the case may be, the immediate present is gone as immediately as it came to be replaced by another snapshot of within the unfolding continuum, there would be no retention of even an awareness of the immediate present, at least practically. Conscious experience, or awareness would be effectively broken; the Real would be effectively unconscious. The only other alternative is that conscious states within the continuum are somehow drawn out, lasting more than a mere instant, but that seems an odd matter to argue. But even then, elongated conscious states of the immediate present, is not sufficient grounds for denying the existence of the Self; the Real. Especially given that we are “aware of our own awareness of conscious states, and transitions between states”, in other words our experience of experiencing experiences, tells us with blatant common sense that we are aware of a continuum, a continuum which we are not reducible to nor reduced to, and so we must have an enduring, unifying, transcendent awareness simultaneous to our immanent awareness of states and transitions; or experiences of reality, including the experience of our own reality. The Real, The Whole, therefore, must be the grounds of its own awareness; grounds which are not reducible to part nor mere sum of any continuum of experiences.
The Real experiences “reality” (including its own reality) within “The Reality”, unifies these experiences; the continuum, and then they become part of the unique history and unique perspective of that Real. This I propose is what makes a Self, a Self; what makes a Real a Person, instead of an impersonal consciousness, or impersonal awareness. And I definitely propose that this is what makes a person existent, rather than an illusory construct of “bundles and habits, or experiences”; or worse non-existent completely.
Regarding the Self, here are the options, and (consequences) as follows;
a. There is no Real.
(a) If there is no Real, there is no capacity for awareness at all, even illusory awareness would be completely impossible.
b. The Real is Impersonal.
(b) Providing for sake of argument that “that Real” did not apply for uniqueness: For the Real to be Impersonal, it must lack the capacity to be aware of immanent experience; it would only be capable of a pure state of “transcendent” awareness - but it would be an awareness of nothing, an awareness completely void of any experience, it would not even be an awareness aware of being aware, it would not even be aware of being aware of nothing. There would be no capacity to experience, as experience (even the experience of being aware) would immediately become part of the history of the Real, unique to that Real and render the Real a person, a self, especially if the Real experienced self-awareness, awareness that it was aware, or aware that it is an entity aware and hence existent. Effectively an Impersonal Real must be practically unconscious, or indeed truthfully unconscious. Existential Unconsciousness, that of a Real existing in an awareness-comatose state of being, is an unhealthy state of being - and seeking to be in such a state is tantamount to Nihilism as it would be an exercise in pathologising experience in order to escape personhood at best, existence itself at worst; and if not Nihilism, existential mortification of awareness itself - an act of violence.
c. The Real is personal.
© Persons exist, Self exists. Personhood, and Selfhood are reality, not illusion; being existent.
In the end, there are only two options which are possible for the Real regarding its consciousness. It is either impersonal, and unconscious (as well as unhealthy), or personal (which is what we tend to experience).
In conclusion, I find myself more convinced of my self. I be, therefore I am.