I posted this on the RPF and didn't get a response, so I'm going to the experts.
I pulled this lightsaber back out to try and fix it. I can't find the paper I wrote the original wiring positions on, but parts of two wires are still on the broken switch. I figured I had a 50/50 chance of getting it wired up correctly, because I know the positions of two wires. Nothing happened. I checked the batter holder in a new Vader FX I had and it works fine and as far as I know the one I'm trying to fix works. So if I look at the new switch, with it oriented up like it would sit in the saber, I've got this (numbered the way the circuit board is):
1 Green 4 Brown
3 White 2 Black
The old switch is like this:
1 Unknown 4 Gray
3 Unknown 2 Blue
The switches look the same; the only difference I see is the new one has a 66 under the switch, and the old has a 65 underneath.
Pics are the pics: