Well my car only has one headlight per side, so inside are two filaments, one each for hi and for low. They ate shifted slightly as to focal length, giving differing patterns down the road. They are NEVER both on at the same time. If the non running High filament droops onto the running low, it will turn on the hi-beam lite, This occasionally happens when the high beam filament gets hot and melts. This makes it confusing, cuz you already know, that Hi-beam doesn't work.
However
I have no idea how the hi-beam lite can come and go, that's a new one.
Ima thinking the foot-switch has an internal problem. I would just stomp on it a buncha times and see what happens.