heater lights, back up lights

Please help.

I own an 87 golf with the 1.8 sohc. There is a backlight for the heater controls that comes on when i start the car and after driving a while it goes out. It only does this in cooler weather. I checked the wiring harness connection and all seems fine. I am worried I may have a short somewhere in the electrical system.

Also, when I bought the car the reverse lights did not work and the person who sold it to me said he would fix them. He did alright, they are constantly on now ( i didnt realize that until later). I removed the bulbs but cannot determine how or why they are on all the time. If anyone has any ideas i would really appreciate them.

One last thing, on the positive battery cable there is a 14 or 16gauge wire coming off the terminal leading to a 6 or 8guage wire leading to a fusable link. A few times now the wire(s) have melted and power to the car was cut. Luckily I was merely driving down a freeway when it happened. The different gauge wires are spliced together and taped. It was like this when I purchased it and am wondering if the melting is caused by juice going from one size wire to the other.

The melting would be caused by a short to ground. Follow the wire to see where it was run to, or disconnect it & see what stops working. The reverse lights are switched on at a transmission multifunction switch. Look on the top of the transmission to the back & right of the clutch cable for the switch. See if you can find where he did the wiring to make them come on all the time.