You said one of the female connectors coming from the wiring harness is 12v hot when the IGN is on. That wire comes from the IGN as I'm sure is obvious. The other wire with a female bullet connector runs back to the reverse lights and then grounds into the frame itself.
Now, it sounds like when in reverse gear your switch is closed and is passing current and heating the wires up? How hot? If the wires truly become hot or warm to the touch you have a short somewhere between the switch and ground.
Also, with the IGN on and one of the female bullet connectors at 12v, I'm not sure how you'd have ground at the switch wires. Without a spark display and or melting wires. 12v plugging directly into a grounded switch will melt your fuse almost instantly, so it's doubtful it's a grounded switch/switch wires.