We've finally gotten all moved and (relatively) settled, and I've got some time to work on this now. Here's a photo of the "original" broken wire I spotted:

This is on the left-hand side of the engine, just in front of the starter solenoid. Notice that there is a plastic connector about 1" from each end of the broken wire; I have no idea why there would be such a short length of wire there. The two connections look like they'd easily be long enough to connect directly without the intermediate connection.
Next up are a couple of photos of the wire that burned. These are on the right-hand side of the engine, just below the fuel-fill:

Note the melted connector and the wire with the insulation melted off.
I've no idea where any of these wires come from or go to. The broken wire in the first photo appears to be white with a red stripe; the burned wire in the other photos looks like it may have been black, but it's hard to tell.