There is a suggestion in DMG on how to handle this situation (DMG, p33):
The game has no rules for trying to stay awake through the
night, writing down every word someone says without a mistake, or opening the stuck lid of a container without spilling a
single drop of its contents. However, in the course of an adventure any of these situations could potentially make or break an
encounter. You have to be ready to make up checks for such non-standard activities.
Using the example situations above, staying awake might be a
Constitution check (DC 12, +4 for every previous night without
sleep), with an elf character gaining a +2 bonus on her check
because an elf is only giving up 4 hours of trance instead of 8
hours of sleep.
While I would not use Forced March rules for this in the nonlethal damage sense, I would certainly request Constitution checks or Fortitude saving throws vs fatigue as well.