Yes, the black plastic thing with the two red wires looks kinda like an automotive ATC fuseholder, though there doesn't seem to be a fuse in it (it should have a 30-amp fuse in it). And the short frazzled red wire coming out of it looks like it pulled out of the red-sleeved connector on the battery positive post, as Kidkraz suggested. In addition, the other red wire is spliced into a black wire, which is probably the main 12-volt electrical feed into the TM. If that is true, then the heavy black wire that connects to the battery positive post through the yellow-sleeve connector is probably not the main feed, but was added by a previous owner to bring power to the jack - which you said works.
The picture is coming clearer. At this point, I think I would put a 30-amp fuse in the fuseholder, and then follow Kidkraz' suggestion to connect the short frazzled red wire to the empty red connector. This ought to bring power into the entire TM, though it will be weak because the batteries haven't been charged.
Try it - let us know.
Bill
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