But that awareness of being different from the mind or watching the mind only comes when I think, which means its mind thinking about mind.
Nevertheless, the awareness/existence does not lose its continuity whatsoever happens.This is known by common experience..(ie. even in the cases of dementia,coma,deep sleep ,etc continuity is not lost forever).Even after dementia, some may get back to normalcy etc , where mind has failed.. The reason for this continuity is attributed to awareness , but it cannot be an entity or a concept (If so , it becomes the object as hinted in Q itself) also bcos Kenopanishad says ( Na Vidmo Na Vijanimo ) that which cannot be known ,being the subject.
But the mind and intellect is experienced/known so it becomes, yet another instrument as in kena up. ( srotrasya srotam manaso mano) the changeless witness principle,which is the observer of ever-changing continuity, contributes to the relativity of change /acting as frame of reference, which is neither non existent( as existence cannot come out of non existence as per vivekachudamani), nor is an entity or concept.. So the conclusion is .. it is the subject that completes the dichotomy (dvandva) of change-changeless..
Yet what ever is to be known can be known through mind only ,
So says amritabindu. Upanishad
mana eva manushyanam karanam bandha-mokshayoh
SVSSS (Sri Shankara Bhagavadpada - Translation Swami Tattvananda)
But the mind (manas) is always conscious, and it understands everything. At the same time it is also capable of comprehending external objects. Would it not follow that it is not prāṇa, but the mind that is the Ātman?(svsss 550)
The doctrine that the intellect is the Self
Such persons might say, “The mind also is but a tool of the Ātman. In this respect it is no better than the eye, and the other sense organs. As a rule, all things that have an instrumental value are for the sake of something else, other than their own sake. Consequently they have no independent existence.”(svsss 553)
Therefore only the wielder of the tool may be said to be a doer; in that sense, the Ātman alone is the doer, for the Ātman alone is independent. If it were otherwise, the Puruṣa woud become a mere agent.(svsss 554)
Infancy and childhood, youth and old age come and go. Waking gives place to dreaming, and dreaming gives place to deep sleep. Good and evil rise and fade away like ripples on the Ganges; but the stream of consciousness goes on for ever. It is in this sense that the Ātman is the witnessing consciousness. It is the eternal ‘I am’.(svsss 614)
The existence of the Ātman is thus woven inextricably with the idea, ‘I exist’; and this concept persists at all the levels of consciousness. That is why it is said that the Ātman knows no change and is eternal.(svsss 612)