The only mechanical car clocks that I have experience with use a small solenoid to wind the clock spring back up; when it winds down to a certain point a set of contacts close together, which energizes the soleniod to wind it up again.
If yours is like this I would be concerned about the contacts wearing faster because of the higher current that the 12V will drive through the coil. You could experiment with running it through a tail lamp bulb or something similar.
You could wire a resistor in series to limit the current, I would start with something like a 10 ohm resistor. Get a resistor with 1 Watt or more power rating for durability and to have thicker leads to work with.