If that's the plastic cover on the left side of the airbox that covers one of the air filter access screws, the plug feeds the tail light. If you are seeing a low voltage there, chances are that the stoplight filiment in the bulb has broken and the end welded itself into the tail light filiment. From the voltage you mentioned, probably close to the grounded end. This could easily pull enough current to slowly fry the insulation on the wire, but not quite enough to blow the fuse.
