I think you can start a game from the lock down button as well the start button. Make sure your problem is not there.

When in test, switch mode do you get :
Tan-white/black white
Or
Grey/Black white?
Without pressing any button

That's the wire to the cabinet start button. You'll need to trace those wires back. Unplug any junction containing those wires, put in test mode, see if switch error goes away I think those wires end up at the circuit board in the back box eventually but I'll double check mine tomorrow. If so I think you can unplug that plug from the board, start up machine, error will go away. This would confirm the 2 wires going to the start switch are shorted

I guess you have a multimeter. Set it to ohms, unplug connection at node board, then test for continuity at the 2 terminals of the start switch. If you have continuity the problem is in that piece of wire between the node board and switch, or the switch itself. If no continuity that leg is OK and the problem is between the node board and backbox. Be careful of the node plugs, it's very easy to replug one pin off which causes all sorts of problems.

Just throw some zip ties on it.

I try to oversimplify stuff because I never know the ability of whom I'm writing to- my son doesn't know which side of a screwdriver to use, so forgive me for that.
You've done well to isolate the problem. If you ohm out where the grey and black/white meet the board...the male plug pins you will find the circuit continuous. My guess would be a bad diode. I'd just buy a new one but you might fix the old for a back up
Congrats on a great game! It's the first on I play every day.