Sounds like the twilight zone indeed. I don't know if I can pinpoint the problem but I'll try by explaining the circuits you are dealing with. Your running/headlights and brake lights should be completely separate circuits. The brake light circuit...power is supplied to the brake light switch, which is closed when the brake pedal is depressed. The brake light switch is then connected to the turn signal switch where voltage is supplied to the rear brake/turn signal filaments, as dicated by the position of the turn signal switch.

For 1957 passenger cars (I don't know about the trucks), the front and rear running lights are controlled separately. When the headlight knob is pulled out one notch, both front and rear running lights should be on. When the headlight knob is pulled out all the way, the rear running lights should stay lit while the front running lights should be out.

All I can think of to explain what you are seeing is the possibility that the running light wire to the rear is getting pinched somewhere in the brake linkage and shorting out. This would explain why the running lights go out and the sparking at the headlight switch when the brake pedal is depressed. Also sounds like there is no fuse protection which is a bad thing. When I restore an old vehicle, I gut the stock wiring and completely rewire, with plenty of fuses to protect each circuit.