Keep in mind that before clocks, the smallest sure increment of time was the day. Basicly you did things based on parts of the day. Like morning, noon (which we now call noonish), afternoon, evening, night etc.
So really you don't need to worry about hours but rather a method to determine what part of the day it is. But then in the underdark there is no day. There is just time. So you would count probably using natural means. In caves this is probably with the movements of water. Drips from a stalagtite, undertides, and the like. Another way is with vegetation. Perhaps there is some plant of fungus that changes colors at a regular interval. If I were using this, I would make all the time measurements arbitrary. So it becomes difficult to tell how long someone has been in a place by just asking them. Five drips from the local stalagtite could be five hours, five days, or even five years.
Aaron.