OK so the mystery wire might well be the one across the top of the picture with a large tab on the end. The size and shape says that a large screw terminal is involved, the length of the wire suggests that it might originally have lived the other side of the bulkhead. It could well be the ground line return for the whole system. Probably a job for a multimeter to see where the 12 volts are going, also, looking down from the 12 volts, seeing where the ground line goes.