Sounds like you have a grounding problem or wires that melted together and are not shorted. I think you will need your wiring schematics and possibly a tone generator to find where the short is.
revisiting this I think there may be some crossed circuits as in melted wires before your fuse box. This would mean the electricity takes the path of least resistance aka the high beam (I am assuming when you headlights are on you have one low and one high beam going and pulling the fuse switches to only low) pulling the fuse breaks this and allows the electricity to flow through the low beam. This is still just speculation though.
If I can get more info I might be able to come up with a more helpfuyl answer.
- if the low beams only are on, which headlights are lit? low beams? high beams? one of each? high and low beams at the same time? some other combination?
- if you switch to high beams, which headlights are lit? low beams? high beams? one of each? high and low beams at the same time? some other combination?
- if the low beams only are on, with the fuse removed, which headlights are lit? low beams? high beams? one of each? high and low beams at the same time? some other combination?
- if you switch to high beams, with the fuse removed, which headlights are lit? low beams? high beams? one of each? high and low beams at the same time? some other combination?