cjoe,
Not sure on the question. The three prongs on the headlight represent two filaments and one common (I think). You should have continuity through each filament tab to the common, or ground tab...does this make sense.
Have you looked at your dimmer switch yet?
I think you will always get continuity to ground, but it must be with a load in the circuit, such as a lamp, or relay. If you probe a wire without a load in the circuit and get continuity to ground, it is a short.
This is what you want to find..a path to ground from a powered wire (not energized) when it isn't connected to its load..a headlight or parking light.
You still need to address the fuse deal, it's your protection and will help you find the problem.
I think this is how it works!!
Stuart