I don't know if this related to the problem you are having, but I have dealt with two separate Dodge trucks (both diesel, one a 92 and the other a 94) that burnt the wiring harness at the headlight switch. In the case of the 92, I caught it in time before it burnt into the rest of the wiring harness. However, in the case of the 94, the problem existed for quite a while before the owner realised it, then he paid a trailer wiring place $600 to "chase down the problem"... All they did was jump a 12V wire to another wire that was supposed to have 12V that had burnt.. definitely created more problems.
I had to remove the whole dashboard from the truck and cut open most of the wiring harness and replace about 50 - 75 feet of wiring. The solution to the burnt wiring harness in both trucks was to eliminate the headlights from the headlight circuit in the truck and run a separate relay with separate wiring and a switch for just the headlight bulbs. With all the running lights and the lights on the roof, etc., the headlight circuit was overloaded. Now when I pull the headlight switch, even to the full on position, that circuit merely runs the running lights of the truck.
The only time there has been a problem since then was with the 94 truck. The owner insisted that since I had replaced the wiring, he once again could run the headlights from the switch on the dashboard.... BZZZZZZZZZZZ... wrong! Once the wiring got hot enough again, the lights started flickering on and off. Needless to say, he went back to my work-around. I had the factory manual for the truck and I couldn't ever find the "headlight relay" in the wiring diagram.. If there truly is no headlight relay, no wonder the damned wiring burns up..
So anyway, if you have one burnt wire, it's rare that you *just* have one burnt wire. Don't assume that is the only one..
That blue wire could be to your trailer brake controller. I rarely see them wired with anything but a thermal breaker, so I believe those wires could go through a cycle of heating up enough times to burn through. And the genii that usually wire the things seem to always jam them through the firewall in the same hap-hazard manner.