Ouch! Never heard of this problem. However, the breakaway switch is open-circuit (never carries current) when the plastic plug is properly inserted, so a short anywhere in the brake circuit would have no effect on the breakaway switch itself. The fact that the plug was melted indicates to me that the switch was carrying full brake current for a long time, and it overheated. This woud happen if the plug was partially pulled - not seated properly. It doesn't take much of a tug to pull it. Unfortunately, if the breakaway switch was carrying current, that means the brakes were fully applied all the time you were driving. The resulting heat overheated the brakes, which melted the grease in the bearings and blew off the bearing cap.
Meanwhile, with full battery voltage on the brakes, the brake controller would see this 12 volts even when the controller is not applying the brakes, and interprets the condition as "Not connected".
If I am right, you may have to replace the brakes and the bearings at least - maybe more. And I bet it didn't do much for your gas mileage, either!
Sorry to be a downer, but I don't see how anything else could have caused the problem you describe.
Bill
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