Have almost the same issue on a 1988 735iL the headlights just cuts out but the fog lights stays on. SO I had to enable the high beams that really is not a good thing. But when click to low beam the lights sometimes comes back on. Mostly happens on a damp or wet day. So in my case something could be grounding it.
They say that the relay switch does not last forever but they are expensive to replace. I wonder if the wiring is worn out. Don't know it has a mind of its own.
So I hope that when my lights shuts of and the fog lights stays on hope that that is not illegal a reason to be pulled over. I'll research some more on this.