Jim: In 1960 Studebaker used very good wire and they used plugs both male and female to make the connections.
You have been given some good advice here though it is doubtful the voltage regulator is causing this problem.
My suggestion is this. Turn the engine off and see if it matters. If the breaker is heating up and moving into the open circut then you have a short somewhere and you should be able to hear the breaker. The breaker is usually mounted on the back of the speedometer head. If you hear the breaker open and close then follow the wires to the headlights. Did you say it did this also on park? If so then check carefully where the wire moves down behind the steering sector and back under the master cylinder and back along the gas tank then at the rear of the truck. You are more likely to find a short if there is one in the rear.
However a 1960 Studebaker is 51 years old. I would replace the breaker first as it could have been weakened over the years and just will not hold the load. It may also be that someone replaced it and it is too small for the load. Ted
Posted on Aug 27, 2011, 8:45 PM from IP address 18.104.22.168