I have a 2000 GC Limited. I have a similar problem since my backup lights don't work at all. I plan to install inexpensive 35 w light units inside the bumper about where the plastic bumps out. I will mount them on the inside of the bumper and cut a hole for them to stick out. As to wiring, I'm not sure if the wire still works, but its located inside the left panel near the tailgate. I need to check the wire to see if it has power; if it does, then I'll wire it directly into the harness. I do not have a trailer hitch or I would go directly to the hitch wire and save me a lot of work.
Good luck with your work effort. BTW, some of the LED lights available now are very bright and would work well as replacements for the existing bulbs. The real challenge is to wire the darn things so they work when you want them to do so.
2011 Jeep Wrangler Unlimited Rubicon.
Wife: 2014 Grand Cherokee Limited