There is no re-personification taking place. It's the body-mind that appropriates "I" (which is, btw., the only perspective there is) in the first place. So, the question is more "who is seeing through these eyes." Not my eyes or your eyes. What we have in common is not the form of consciousness but consciousness itself. Strictly speaking there's no such thing as form of consciousness, because "I" i.e. consciousness is without attributes (though, ironically, all forms are consciousness/existence) But that too is misleading, because even more appropriate would be to say that there's only I and all eyes are me. Am I a vessel for myself? Am I two? Obviously not.

Also, the realization I'm talking about is not some kind of peak ecstatic or other mystical or religious experience. It's not even an act. More a lack of it. You may try an experiment--simply observe the world in its entirety. From gross material to subtle mental phenomena. Obviously, what you can observe is not observer (and, mind you, "I" can observe even absence of forms). Who then observes?

There is this expectation that there is some impersonal consciousness somewhere to be found. That after abandoning the ego a dissolution of identity takes place. Sure, one stops to identify with all kinds of BS, but consciousness is as personal as it gets--without "I" no form would have any identity to begin with. And since you too refer to yourself as "I", there's no doubt that you can know it/yourself (well, essentially, me :D).