But can a bigger system have consciousness when individual parts of it are already conscious? I don't see why this should necessary follow. I'm sure there are somewhat similar and interesting emergent properties, but we'd probably call it something different. Probably closer to the kind of group identities we already have with lots of humans interacting. Though obviously we'll know what it feels like, just like none of my neurons will ever feel like i do.
If you had a physics model it could describe it perfectly but it would likely involve a very large group of matricies and linear algebra constraints. You technically could work through every equation given a large set but examining the watch yourself would likely be quicker, if not learning to be a sufficiently good watchmaker.
However if you assemble a computer model to handle every component's interaction individuallt and a physics engine to do number crunching you could get a working mathematical model of the clock.