Ignoramus8558 wrote:
[...]
My problem is that the DC motor (pulled from a demolished HP X-Y
recorder) would overheat from being under power constantly.

I would like to find a little 12 VDC motor that could survive a locked
rotor condition indefinitely, or some other simple solution. A little
solenoid with a dual coil (pulling and holding) also comes to mind. I
need something that can be bought for a few bucks at most or made
easily, and I am out of ideas.

Maybe add a cheap linear regulator and either use the built-in thermal
shutdown protection or wire the regulator as a current limiter. Look up
the National LM7812 etc...