Re: Problem with Low Beam Headlight Wiring
One of the "wizard ideas" that came along with computer aid design stations and whiz kids to run them was absolute minification of all components and wiring (to save weight and cost of course ;-) ). Unfortunately that leads to problems when "unapproved" situations arrive. In this case, the wiring is sized JUST EXACTLY ENOUGH to handle the OEM wattage headlamps. Sticking on a load heavier than that (i.e., 80W or 100W) is just asking for trouble.
So, you stuck in high-wattage lights / lighting systems and had problems. Intermittents? Dimming? Not working at all?
(1) You probably damaged the modules that drive the headlights as they are designed to deliver only the proper amount of current and the output transistors or whatever they're using will be rated thusly. A heavier load will cause them to overheat and/or burn out. You CANNOT get around using the factory modules because of the way vehicles are designed now. Don't like it? Buy 1950's Chevy's. Yes, the designer could have anticipated this misuse and used heavier duty components or designed in a thermal protection circuit ... but the bean counters would have just over-ridden this in the name of cost-savings; so they didn't.
(2) As long as the module hung in there delivering more current (aka, power) that it was designed to, the minimum-sized gauge wire was overheating (i.e., the blackening and charring some note). It is quite possible that in some places some of the wire has actually melted inside the insulation (hidden from you) thus the dimming and intermittency (as vehicle vibration causes individual strands in damaged sections to brush by each other and make intermittent contact). A resistance check is likely to be of little use except where the wire is completely burned out. Harness replacement is the only reliable way out of this mess.
Still hell-bent on sticking in big wattage lighting? Make sure the manufacturer is using an auxiliary relay-powered design; or is willing to pay for any damages to your Jeep (including modules and harness replacements) over the next 12 months / 12K miles. Yeah. Good luck with that. ;-)