Q:

Is it possible to create a consistent timer using only gravity?

I've got a cave civilisation who have never seen the Sun, and don't have much of a concept of time. I was inspired by a Reddit post from someone with a similar situation, and like me, the OP was wondering how people can keep time underground. Someone suggested sand timers, water timers, etc.
What I want to know is: is it possible to build a timer, e.g. a water timer, which dripped from a top chamber to the bottom chamber, in such a way that it caused the whole thing to gradually rotate by itself? I.e. without a motor? Because I could say that the civilisation has tech and can create motors or electricity, but on what basis would they have to time the motors? How many "seconds" (for they won't have a concept like that,) would they decide is needed before the mechanism turns the timer? The only alternative I can think of is having one person who turns the timer every time it reaches the bottom, every day, for the rest of their lives.
So it would be cool if it were possible to build a timer which rotated by itself, simply using the flow of gravity. Is such a thing even conceivable, let alone possible?

A:

You need to have some energy input from somewhere. Without that, you're trying to build a perpetual motion machine, which is notoriously difficult.
A more conventional route would be to discover that pendulums move rather regularly, and then discover the rotation of their planet, via the Foucault Pendulum experiment. That should give them the motive to invent the pendulum clock. 

