Actually, the circuit is a variable oscillator controlled by the adjustment of a potentiometer that controls the charging of the capacitor; that RC constant controls the oscillator (similar to a multivibrator), which is configured to dump the charge to activate a transistor that activate the relay which connects the wiper motor to the battery (there's also a switch contact involved that opens when the motor has completed one revolution). A simple circuit details this:

http://www.eleccircuit.com/wp-content/uploads/2007/10/index....

Kearns' patent essentially shows the same kind of system:

https://www.google.com/patents/US3351836

I find it interesting that he did design it this way, as production transistors at the time were still fairly "new" on the market, and would have been an expensive component. There are probably ways to design it back then that wouldn't need a transistor - perhaps based on a bi-metallic switch plus resistance for adjusting the time for a heater to heat up (basically, re-using an automobile blinker in some fashion?) - though maybe this was the direction Ford was trying to take, and Kearns was able to use the "new-fangled part" to his advantage?

Oh - in case it hasn't been posted yet - the New Yorker article the movie was based on:

http://www.newyorker.com/magazine/1993/01/11/the-flash-of-ge...