Steve,
I cannot tell you what the system is that had the wire burn up, but your instinct is probably correct. It sounds like this wire could have had the insulation wear through. You described that the insulation melted off. It seems a litte strange that this would take place while just sitting still, so be a little suspicious about that being the root cause. You do need to find the root cause to be comfortable that it will not happen again.
You should be able to take an ohm meter and measure across the coil of the solenoid, with it disconnected, and also measure from a coil lead to ground. You should see some relatively low ohm value, I'm guessing 6 ohms or less, more likely 2 ohms or less if it is a big solenoid, for the coil resistance and a very high value, maybe infinity on the meter measuring the coil lead to chassis ground. You are checking that the coil is continuous, not shorted due to insulation melting, and that the coil itself is not shorted to ground. If that is O.K. , replace the wire and try the motorhome systems until you get that solenoid and pump to function. If it operates normally and that wire is not getting excessively warm then you should be good to go.
Consider also that the wire could have melted due to the 7 or 8 minutes of operation of a system that was not meant to be run continuously, like a starter might do. I think that is not the most likely case but you need to be prepared that if this solenoid/pump started to run again on its own, that you have a game plan to shut it down with switches at the battery or by disconnecting it if that is what really caused the wire to burn. That would then give you time to sort out what is causing this circuit to fire up. Hope this helps.
Later Ed