I just went through this very thing. The 03-05 trucks have relays in the PDM (fuse box) that control your left, right and driving lights. The relays go bad. Couple years ago I split the fuse box open and replaced the 3 relays with the 30 amp Zetter relays. Problem solved, for a while.
Within the last year I have been having intermittent issues with my right trailer turn/brake light. When you have your turn signal on, take the cover off your fuse box and listen. If you hear clicking from the fuse box you either have a bad contactors in the relay, or a broken wire. Most likely you will hear nothing. If that is the case check fuse #46. If the fuse is good then you may have a bad relay, PDM or FCM. In my case it turned out to be the FCM acting up.
One of the most stupid designs I have ever seen.
I finally got fed up with it and installed one of these and remove the trailer light function from the PDM altogether.
https://www.napaonline.com/en/p/TWR48000
If you are trying to check for voltage at the plug on the rear bumper, the factory wire colors on my 04 were yellow (left turn/brake) green (right turn/brake) and brown (driving lights). I was amazed Chrysler used these colors.