Good thought, but I think even a very precise timer would eventually get off in one direction or the other.
Well, I ordered a dual-coil relay and tried my last design out on a breadboard using a dc power supply. The fatal flaw in the design seems to be that the relay doesn’t disconnect when the negative side of the coil is disconnected. So the motor keeps going around and around instead of shutting off when the switch is reached.
In fact, I can make the motor work both directions without hooking up the negative terminals at all.
Are relays supposed to trigger if you only have the positive side hooked up?
The relay coil needs a return path. I have seen things such as relays and electromagnets work with the neutral disconnected. It is getting a return path, just not through the conductor. It could be returning through whatever it’s mounted on for instance. It’s such low current that it won’t take much of a path to work. You might be able to isolate the relay from the backplane with a piece of rubber as a start.