OK, so the capacitors are evidently not the only failure mode.
My clock ran perfectly. Some months ago I took out the clock to install a Rennline phone mount I bought cheap on the board. Why? I don't use the phone in the car. Well, because it was cheap. So on reinstallation, the positive clock lead touched the (already grounded clock case, made a little spark, blew the fuse, and that was it.
The clock ran intermittently from that point. I consulted my favorite forum, found this thread, replaced the capacitors, and reinstalled. Unfortunately no change in behavior. The clock ticks always, but when it ticks loud the hands move, and when it ticks quietly they don't. At this point, they mostly don't.
So does anyone have a spare mechanism? A spare clock? I know I can replace capacitors now....