Brion
Hello & Welcome to the Forum!
A "little" 8E SG, how cool. They were the smallest locomotive in the SG line.
The switch you wonder about is a manual reverser.

I've added a link that should have answers to every thing you need to know.
http://slivideo.mobi/online/1286454-lionel+8E

For parts, I suggest forum member Bill Hennings' family' shop:
http://www.henningstrains.com/

On that wiring, if it's old/original wire, just unsolder one end, slip a piece of shrink wrap over it , then reattach it.
your problem may be that  broken or missing wire insulation/coating is causing a short.

Happy Rails
dave