Check the outputs on the receptacle mounted on the truck. If they work, the truck is fine. Then light up each circuit on the trailer by applying 12V to the terminal in the plug and try the ground both at the plug and directly to the chassis.
Problem is that all the lights on the car/truck do not work off chassis ground. Voltage is always present at one side of the bulb and flows when switch of one description or another completes circuit through one of the black boxes up front. It all operates above chassis ground. Using chassis ground on a trailer really mucks things up. ( have to go back a lot of years now to find a chassis ground operating system on vehicles- pre computer days). Not all after market lighting units account for this. In other words the lamps on the trailer should be isolated from chaissis ground and only work through the harness. Unless you keep the connectors greased ( conductive grease) they will go bad in a season and deliver all sorts of headaches for yourself.
Used to have the same problems with trailer lights and gave up. Went to U-Haul and got a high quality set of magnetic trailer lights and just unplug and keep in the garage until I'm ready to use the trailer. Been working now for three years without any glitches.
Having to drag out mag lights and secure the wiring every time I need the trailer would drive me batty. After one or two occurrences of that aggravation, I'd be more than ready to re-wire the SOB. Head on over to etrailer and check out what they have for wiring kits. You can by bonded 4 wire harnesses, connectors and junction boxes all ready to go. You can make it as simple or as complicated as you like. I would get some HD cable rated for outdoor use or put the 4-wire bonded stuff in some kind of conduit. No scotch lock connectors either. They can be used successfully but never where there is moisture or constant heavy vibration. So using them on the trailer is out! Any permanent electrical connection on the trailer should be a non-insulated crimp connector crimped with a tool that makes the connector into a B type shape. (Folds the tabs over in the center) then solder and shrink tube over top. I would also consider wiring the trailer to a junction box on the tongue and using a separate pigtail to connect the truck to the trailer. That way if you ever damage the connector or pigtail, just unscrew it in the junction box and toss it. No need to splice the new one in, just solder on the terminals and connect it.
It's amazing how many of these lighting problems could be prevented because people don't. Great idea.
Heh, guess I forgot a link for y'all. my favoritest truck/trailer site in da whole wide world.... http://www.etrailer.com The wire - 4 strand bonded: http://www.etrailer.com/Accessories-and-Parts/Deka/16-4B-1.html 4 strand jacketed: http://www.etrailer.com/Accessories-and-Parts/Deka/DW03240-1.html The pigtail/connector: http://www.etrailer.com/Wiring/Hopkins/HM48030.html The junction box: http://www.etrailer.com/Accessories-and-Parts/Spectro/38656.html Or if you want to do it on the cheap, just pick up one of these: http://www.etrailer.com/Wiring/Hopkins/HM48240.html
Electrical problems in a Chrysler Jeep? Naw!!!!! No possible way ever. I had to rewire my zj's trailer harness after the factory one gave me fits like you are having. I ended up using a harness / box converter that had a wire that went to the battery. Now, the lights on the trailer stayed on all the time they were connected to the pig tail, but that was the only issue, and I could have adjusted that, but I didn't care enough to redo that. The lights on the trailer never had an issue after I put that in.
Something else to consider ,Hopkins 4-Way Flat Trailer Connector w/ LED Test Lights - Trailer End - 24"
This was pretty much what I used on my zj. http://www.etrailer.com/Custom-Fit-...erokee/1997/C55260.html?vehicleid=19971173542
This is exactly what mine had on it when I got it , http://www.etrailer.com/Custom-Fit-Vehicle-Wiring/Jeep/Grand Cherokee/1995/C55349.html?vehicleid=19951173543 and a Curt hitch http://www.etrailer.com/Trailer-Hitch/Jeep/Grand+Cherokee/1995/C13151.html?vehicleid=1995202632