Yep, no “me” observing the passage of time, and unless one ascribes to a ghost in the machine – a element of “me-ness” that exists outside of the conscious, thinking me – then that’s all there is. No conscious me == no me (for that time).
I have the odd experience of having a (smallish) piece of memory missing a decade after an accident. I was only actually unconscious for less than a minute, but to this day am missing any conscious memory of a period from about 20 minutes before the accident until about 3 hours after. It’s just a big blank spot.
It was a weird experience having an accident inspector explaining to me what I apparently did that contributed to / caused the accident, but with no memory of the events to attach this to, and no way of feeling any emotional response… that and seeing the film footage that the camera crew covering rescue helicopter operations shot; seeing yourself apparently conscious and (mostly) coherent, and yet having nothing to attach it to in your own internal record.
While I’m (still) not prepared to make absolute statements that I know what happens after death, I am pretty sure that for me at least my “me-ness” consists of my conscious thoughts and contiguous memories. Take those away and there is no me, and I expect that dying is the same thing.
And yeah, I find that pretty scary and don’t choose to dwell on it… but the fact is, if I’m right I’ll never know about it.