First I have to ask, Did those turn indicators went back off when you went back to low beam ?
Here's my guess...
The problem is chassis ground(s) at the radiator core support. Current will seek and use any path to ground it can find. High beam light current used the park/turn fixtures for ground. The low beam probably does the same just not so bright that you notice it.
If cleaning/improving the grounds out there doesn't cure the problem, you'll need to
start looking at the positive side of the circuits, starting with the harness connector on the headlight switch. It may be melting.