Yes, a few of the later ones. They're electro-mechanical. Test the electric first. Usually one hot lead and the case is ground of course. If the relay is burned, find another clock. They need a 1/2 amp fuse added to the power feed. The mechanical part is usually actually easier. Careful on the disassembly of the case - the metal tabs often break when bent. You have a relay with a contact on an armature. As the main spring winds down - about 2 minutes - the contact energizes the relay and winds it up. As long as that part works - carefully remove the second, minute and hour hands from the mainshaft. Clean in alcohol, drop some neatsfoot oil on the jewel and reassemble.
Maybe I've gotten lucky, but I have fixed two of them pretty easily. As Demonic pointed out, they are electro-mechanical. When new, they had some light oil to lubricate them. That oil gets dry and old, and stops the movement. I have had great success with some careful use of carb cleaner and some fresh, light oil. That's it, and bang, they are working again. (They are very easy to bench test too.)
For whatever it's worth, I posted this video a while ago on You Tube showing what the inner workings are on a 66 or 67 Charger console clock. It shows how the solenoid and points work to wind the clock. This winding sequence happens about every 50 seconds or so..