Code, I haven't really looked at the wiring for headlights on our trucks, but I had a similar problem once upon a time in an old Mercury. I was driving to work one dark morning and the headlights went off, came back on, and repeated this behavior. I discovered a damaged wire (insulation worn that was letting the wire short to ground). This caused the headlight circuit breaker to trip. Then it would reset and the process would repeat.
I imagine worn insulation in the vicinity of the multi-function switch would present similar symptoms, rather than a "broken wire".
I'm not nit-picking here, but a broken wire is easy to spot. A damaged one may take some careful inspection.