I am sure plenty of folks have been down this path. Eight years ago, I bought a custom headlight harness from a forum member. I regret that he has since passed away. I bought it and a few other things for a brighter headlights project on my wife's Waggy. It ended up sitting in a box. That happens.
Fast forward to last month and there is a short in the headlight circuit trying to melt the headlight switch. I discovered the factory light harness splices bare and touching metal on the front header panel. The soldered splice had lost it's factory duct tape and the loom was rotten and falling apart. Must be time then.
Right away I found two wire connection on the low and high beam relay plugs were broken. A friend came by for a visit so I enlisted his help. We got the connections fixed. We got the new harness installed and began troubleshooting other issues right away. The new H4 lights did not fit the headlight buckets. They got modified with a zip wheel so they would fit. H4 headlights got installed but the the lights were not consistently working correctly. We came across two other connections to the relay plugs broken and fixed that. There was still trouble with the lights working consistently. Finally, we realized two wires were swapped on the Hi beam relay plug. Got those swapped and still had issues. By then we were on our second day of work. Finally we figured out the relays will not work right once the battery voltage got down to under 10 volts. Threw a battery charger on and WAH LAH! To be thorough, the headlight and hi/lo beam switch were also replaced with new ones.
Wifey is going to really like the H4 lights compared to the yellow headlights the Jeep has had for so long.