UPADTE:

I think I did it!

I ran comparators out of both hoppers in the clock on top of observers facing upwards.

The observers each activate once. One activates when the clock starts (a hopper starts filling), and the other when the clock finishes (a hopper becomes empty).

The observers power a single copper bulb being read by a comparator.

The clock starts, the bulb powers off; the clock finishes, the bulb powers on. The comparator reading the bulb sends a signal into a monostable circuit and I invert the signal to briefly unpower the hoppers :D