If I had nothing to start with I'd probably just twist the wires together and tape them up. Otherwise I'd go with what was in place, as long as it wasn't something terrible. That three-wire thing in your image doesn't good to me, but if there were two in place already and I'm supposed to add the third, I'd probably do it.
Ok so we seem to be on the same page with everything. I like your paper copy of the manual with the color coded wiring, I have the black and white on my phone. I think I will just buy a whole new inline fuse, heat shrink and really seal it up. Thank you for your help.