I have seen just this happen when the high beams and low beams stay on at the same time. It's hard to see, and the high beam indicator would also be on. It puts a high load on the ground wire and all other components in the circuit.
In fact I just found this very problem on a 55 Porsche speedster last week. The high/low floor switch was bad, allowing both high and low beams to get power at the same time. The switch was replaced about a year ago. The root cause of the problem in that case was undersized wires to the headlights... they caused too much resistance and overload on everything in the system. I don't know what gauge wires you have going to your headlights, but they need to be pretty heavy. The ground wires as well.
ASE Master Tech
20 years of automotive repair & modification, USA, Asian, Euro, old & new cars.