The current is measured in amps, think of it this way, a water pipe, volts is water pressure, current is flow rate and resistance is the size of pipe, if the switch contacts are dirty they cause resistance, if any of the connections are dirty they also cause resistance, so the flow rate increases, this causes things to get hot, the switches have a tendency to melt because they dont get serviced or more specifically, cleaned. Just like your connection got hot and melted due to dirty contacts. Electrical systems need servicing just as any other part of the vehicle do, and when installing new systems they need to be done correctly , or they will fail , just as yours did.
I reckon you have three options, return the system back to factory and give it a right good service, repair and put the harness back in service, or, modify the harness to make it safer, I would probably modify it if it were me, its already in there , you know how it works and you know what to do to make it better.