Does it matter what exact time thinking occurs? If so then humans have nothing productive whatsoever to say on the subject, because our thinking is massively distributed with all the parts of it happening on different delays and competing for conscious notice that most of it never gets.
Some of it definitely happens when you are unconscious -- sleep is necessary for some forms of learning to occur, which has been verified experimentally for various strategic skills. And we sometimes make decisions while we sleep, or when we think we are idle and not thinking, only to realize we have already made them once they become relevant.
Totally non-autistic people seem not to pay a lot of attention to their own thinking, and folks largely reject these facts, but we have enough data from psychology now to confirm that thought really happens this way, and not the continuous way everyone talks about it happening. The continuity is an illusion we construct to improve communication, and not an actual experience.
Working from there, if the doubt occurs, you have been conscious, whether or not you are right now, and setting the exact parameters when you are doing the thinking is an idealization that just does not fit the observed facts.
If you go back and forth between being dead an not being dead, then you do in fact die, you may just not do so permanently.