Wiring trouble shooting question

Thanks for the direction. I looked under there before but didn't see any cream colored romex matching what's inside! Just some 12v wiring and a black round rubber hose looking thing. But I think the black is the 120v wiring?? Looks like a pinch in the wiring exposing a hot wire.

So now, anything in particular to pay attention to for the splice, since it runs outside? Basic pinch connectors ok? Do I need to tape and isolate it back up like it is in the rubber hose?