You can buy a good standard light wiring kit at Wal Mart, and you can also buy NOW (not just a few years ago) a heat-shrinkable crimp splice somewhat similar to the ones we use in aircraft "Environmental Splices". Forget soldering.New wires, solder and heat shrink. Then you don't have to worry about it again.
I suggest replacing the wire. But, if your not you can trace em down easy.
Take a new wire from ground on a battery and touch it to the trialer. Take one of the others and touch it to pos. Look what comes on. That will tell you what it what. I am sure the white on the trialer is ground, so do that last. If all the others are figured out, dont do the white one. .
I have done this before and was a lot easier than tracing the wires by hand.