If can replace the "flip dot" with an electromagnet that opens a gate and makes something (e.g. ball) fall through.
The electromagnet may take 10mA or so.
A simpler solution is to involve a battery powered quartz clock. You power the clock (so the seconds hand moves) for as little as possible at the end of the time-cycle, but as much as to make a visual difference.
Interesting challenge, I would like to see it working in practice.