When I was a kid, my dad (a physicist) would often read stories to me and my brother. He would sometimes fall asleep while reading, and we could tell when that was coming because suddenly our children's story would stop making sense and get filled with all these big physics terms.
That is an amazing sleep indicator: once the rabbit starts discussing thermodynamics, dad has left the building
Oh yeah, I have been sleep deprived so much that the things that I said made no sense. I still formulated sentences but they did not have any meaning. In fact, I noticed this myself and I was like "fuck, what I just said made no sense". This happened a few times. It is a pretty interesting experience.
Somewhat related, but when I was sleep deprived and falling asleep during a general relativity lecture in college, I caught myself reasoning through the series of equations written by the professor on the board, and agreeing as to their validity with the explanation in my mind being that my parents are in a foreign country. My brain was convinced it had logically checked the progression and that it made sense, but it was based on this irrelevant fact. The experience always makes me wonder what falsehoods we individually or collectively use to convince ourselves of things being true.