So at work I got a clock that has a problem. Batteries go flat regularly, and it randomly stops running. One of the new "continuous movement" types, which seem to be the way to use a battery a month. This one uses an AA cell, and it generally will last a month, but recently it was stopping, and rolling the cell would get it running again. Not a good thing.
So, after getting the $5 replacement, with a new AA cell, I decided to improve this one. Gently unscrewed the front glass, remove the hands and undo the mechanism, then pop the 3 clips and take it apart. Inside a green blob on a small PCB with dirt on the pads, so there is the intermittent. Soldered on wires to the pads, and gently get the pieces back together, now with 2 wires leading out. Then use DMM and the nearest red LED ( that is why it is 10mm, nearest one to hand in the box of random parts) to see which pad was positive. Turns out it was white lead. Then into the eWaste bag to grab a resistor and a capacitor, found a sony board with a 1000uF 10V ELNA capacitor on it, along with a 5k6 resistor, so these went on the clock as voltage regulation.
Capacitor across red led means the current pulses during the 8Hz tick are easily supplied, even though the LED current is around 1mA. Now it is powered by a solar panel 12V system, that provides radio and lighting for me, so I can ride out power interruptions and also save on the power bill, so I never need to buy a new battery for this clock again.