I keep thinking about this but I forgot to mention it. There might be a short in your umbilical. between the plug and the junction box. Is there any damage or repairs you can see in the cord? Has the plug been replaced at some point? Or is it still the factory molded plug? If the cord is damaged you'll have to either carefully slice it open and repair. Or just replace the cord and be sure it's right.This is the one I used to replace my cord and I'm very happy with it.
LinkTie some strong cord to the wires in the junction box before you pull them all out of the trailer. Then you can hopefully use that same cord to pull the new wires into the box.
Edit: I just realized you gave us some information that we all missed. When you plugged the umbilical in a second time you had more lights working. I've been in your shoes before and you have a worn out socket on the truck or worn out umbilical plug on the trailer. So unfortunately any umbilical tests inside the trailer are suspect because you can't be sure you actually have a good connection at the truck end.