When I find myself as pure awareness (which already there leaves the rest of Existence out), I find myself also as apparently timeless, free of any coming and going.
I am always awareness, although sometimes my human self lies down – and there is an abrupt change in the external situation, for instance from darkness to daylight. Even here, there is no sense of a gap, although it may appear so to anyone watching my human self lie down and appear to have no awareness of what is going on.
So from my own experience, there is no gap in awareness, there is no coming and going. From the view of others, there is.
And this is one way of looking at this Zen death poem…
When I die, I won’t go anywhere, but if you call my name, I won’t answer.
(Another is that when I fully awaken as pure awareness, present even when my human self is asleep, then I continue to know myself and be present as pure awareness even when my human self dies the final death. There is an unbroken continuity in another way.)