Conley0619

We have an 85 Mustang Convertible that we are trying to fix up for my step-daughter to drive. There is a problem with the highbeams that we can't figure out and thought maybe someone could offer an opinion. High beams will work for about 20 minutes and then all lights cut out. Flip the switch to low beams and those come back on. We replaced the switch in the column, also replaced the headlights, same results. When the switch is held, the high beams will stay on. Also, they sometimes will go back on after being off. Any thoughts on what else could be the problem? Won't pass inspection until we get it fixed and really hate the thought of a huge repair bill. Thanks for your input.