With the battery negative disconnected, is there any conductivity between the low-beam and high-beam at the headlight receptical? How about when the dimmer switch is in the other position? (I wonder if you are actually trying to run both high and low beams at once)
Kinda high. How much voltage with the engine off?
How fast does the fuse blow? Immediately, or over a while? What is the amperage of the fuse installed? Will you burn out a fuse if you have only one headlight connected?