rear light harness melted. what options do i have to fix it and what causes it?

[bongo]

i had a check tail light , then check brake light warning on my 2001 4.4 e53 display. also the rear indicator has stopped working.
i checked the bulbs etc, and noticed that the plug connector has melted where it connects to the rear lens. its the thick brown wire.i just want to double check that this is the ground?
the wire looks ok. can i bypass the connector and solder a wire from the ground to the bulb housing as a quick and cheap fix.
what other options do i have?
also what causes this, i see it is a very common problem.
thanks