I can solder. I'll look at this option. My assumption is that I'm going to solder what leads to that board with what leaves that board bypassing it all together?
The problem is that when there is no sound, then the grounds are connected to live. In electrical jargon this is switch contacts closed (shorted) circuit. When you have sound, then the contacts are open circuit. (signal passes through).
To make sure you don't have trouble down the road, I would use a standoff strip like this.
You can order them here.
So, trace the arm wiring to this switch and unsolder the arm wires and the leads from the switch.
Find a suitable place to bolt one of those standoffs to the chassis and then solder the 8 leads to the standoffs, to make a reliable permanent connection.
Now pick up wires are frail and trying to strip the insulation can damage the wires.
The best thing to do it to get a lighter and burn the ends of the wire and then the burnt insulation will crumble in your fingers and you have a nice clean wire to solder.
You are not a moron at all. You are doing very well. A project like this is a really good way to learn new skills and gain experience. If you keep your heard and continue to ask questions, you will end up with a very nice unit. We can guide you there, I'm certain. This turntable is worth the effort. In the end it will sound a lot better then it has done in the whole of its life.