Ya, the clock hour hand thing was just a kinda silly thought on my part.
The second thought...if you had the tools and knowledge (which is the expensive and time consuming part), a small MCU, a few MOSFETs, and some glue-y parts, that would be the kind of thing a guy that was into it could throw together with parts on hand from the bin. But again, gotta have the spendy stuff first to make the cheap stuff.
Sorry...I hate it when people do that to me
That diagram up in post #12 looks like just the thing you need. If the motor spins too fast, put a big ol' (meaning something that can handle some wattage, not a high resistance value) resistor inline with the motor to slow it down a bit...maybe just a simple 12v light bulb would do the trick.
And if you can't find reed switches to handle the current, then maybe just use a couple slabs of copper to do the job. Go all "Red Green show" on it (being from WV, you might not get the reference, but us from up north should get it).