1. Do quartz watches commonly have an adjustment for regulating them?
2. How can I pick up the signal from the quartz oscillator and count it?

So far I've been unable to pick up a signal with a simple loop. I assume
such a signal is at 32,768 Hz, and that it must be amplified to drive a
counter. The trouble I see, is that one Hz error at this frequency
corresponds to a significant error over time.

Fred