This's the tldr, but if you want to see the details, see here:
http://www.lighting-gallery.net/gallery/displayimage.php?album=308&pos=0&pid=137975
Basically I got this over the weekend and no matter how I hook it up it runs too fast. I did some research and saw something about this being part of a master slave clock system but I can't find any info on this specific clock. Tia

This is a slave clock of sorts, the 10rpm motor would be connected to the master clock for setting it to the correct time.
If only the 1rpm motor is connected to power, it should keep correct time.
Is the 1rpm motor running OK? Could need oiling.

Just checked, and the gearbox on the 1rpm has failed somehow. I can't get it apart to fixed so I'm now on the search for anew motor.

Just checked, and the gearbox on the 1rpm has failed somehow. I can't get it apart to fixed so I'm now on the search for anew motor.

Loosening the screws on the gearbox perimeter does not work for the gearbox disassembly? There is high chance the old lubricant just degraded and got sticky, so a good wash of the internals with some low viscosity oil should make it free again. Because of the two motors, I would expect there just some simple planetary and maybe some worm gears or a similar "puzzle" assembly, so no springs throwing small parts everywhere whe the last bolt of the case gets removed...

These have a very small sealed gearbox attached to the motor to reduce the speed to 1rpm.
Often the gears are just worn to the point where they no longer mesh so the motor spins free but the gears don't turn.