There is a book with the list of who has watch when. The guy standing 0000-0400 would wake up the next fellow at 0345.
About falling asleep on watch…
There were a series of escalating punishments that were given out for minor bootcamp offenses in the Navy. Most minor offenses were treated with on-the-spot “MASH”, Make A Sailor Hurt. This was pushups and the like at the CC’s command.
Individual offenses were often treated with the military equivalent of detention: “EMI”, a.k.a. Extra Military Instruction. This involved cleaning heads with toothbrushes and the like (I did this one a few times).
More severe offenses received IT (Intensive Training) which meant you would go to some secret place in the evening, with all of the other unfortunates, to do painful calisthenics. There was another level that started with an “M” (“military motivational unit”, perhaps?) They said that this was far worse than the IT previously mentioned. They would do lots of exercises with their rifles and such.
Next steps involved ASMO, which stood for Administrative something or other, you would be held back several weeks in your bootcamp training. Since it sucked so bad, no one wanted this. After that, if you continued to be a problem, you would be separated from the military.