Good point. I'll disconnect the lights from the controller tomorrow.I didn't notice that other cable. If it's pinched and shorted. I would say there's a pretty good chance that it's the source of your problems. I'm not sure it's damaged where tied, like it shows in the photo, but could be damaged somewhere else. It can be easily eliminated by disconnecting it from the controller.
Probably been like since the bike was built was built though, it's an o.e.m part.