66 coupe electrical problems

I would bet it is the headlight switch which has a built in circuit breaker. It is about 25 dollars for the part and pretty easy to change out.

Here is the factory manual for Lighting to help you step by step;
Group 15 Lighting, Horns and Instruments

Try replacing it first. If it still does not work you have a short or grounded wire and then it will be onto trouble shooting which circuit it is. If you turn on the headlights and hear a clicking noise every few seconds then the circuit breaker is cooling off and tripping again on overcurrent.
Here is a schematic of the the circuits:
http://hammar.dyndns.org/~djhamma/wiring/1966/66exter1.jpg
http://hammar.dyndns.org/~djhamma/wiring/1966/66inter1.jpg

Good Luck and be safe
Ron