As Attila says, hard to diagnose without the guitar in hand.
Explorerlover wrote
When I touch the switch, I get a serious buzzing/humming racket but when I hold it with both hands ( and pluck the string ) all the issues disappear and the guitar sounds like it should.
This is key. Sounds like a bad connection at the output side of the switch or a bad switch. Redo the joints, but don't just ADD solder, remove most of it and replace with fresh.
If it could be moving the wires around at the other end that solves the problem, then check the joints on the other end of the wires too - specifically the output wire (as the problem affects both pickups).
Also check for earth wires that have been overheated and melted through the insulation of the core wire. That's a common fault.
There is a ground wire running from one of the stop tailpiece posts to the tone pot
Not a crucial connection - more to earth
you (so you act as additional screening) than the guitar.
2. I've heard of star grounding, but where is a "easy" spot to ground everything at once?
Not essential in a guitar circuit. Can be nice from a neatness standpoint if done correctly, but doesn't do much (if anything) to improve the earthing.
