Vintage analog car clocks function just like the Big Ben clock on your nightstand. They wind up just like the gentle Ben, and they have a balance wheel that rocks back and forth with the help of springs, gears, and rods, just like the wind-up household special. Where Ford car clocks differ is how they are wound up. The Big Ben on your nightstand is wound manually every few days with a key on its back side. Forget to wind it, and the ticking eventually stops.
Then you oversleep and are late for work.
Car clocks utilize an electric solenoid (relay) triggered by contact points that come together gradually as the clock ticks. These contact points are like the ignition points in vintage Autolite and Motorcraft distributors. They make contact and carry 12 volts to the rewind solenoid. When the points touch, electricity travels to the solenoid, which kicks the contact-point arm back to its original position, rewinding the main spring in the process. Car clocks were wound up at the factory to begin with. The occasionally energized rewind solenoid kept these clocks wound.
Most of the time, car clocks quit because the rewind process stopped. The rewind process stopped because contact points became corroded or pitted. Corroded points became incapable of carrying electricity to the rewind solenoid, rendering the clocks useless. Most often, we can get them back in operation by cleaning the contact points and spraying the movement with tuner cleaner and WD-40.