The power jack and all lights on the front of the trailer work on the battery, and the interior light in the storage compartment works on the battery. Nothing in the trailer on 12v has been noted as not working when on battery only.
In taking a closer look at the wiring, it does not appear to enter the trailer at the location of the wire, but rather runs off to the right(from the perspective of facing the trailer front) under a covering(so that the wire can no longer be seen). Also, I got no indication of voltage by testing with a multimeter - but the contacts in the connector are so small I can't be sure I made proper contact.
The wire in question is the one at the top of the picture.