The tact switch pins 3 and 4 are just connected to the ground bus, so you can just connect one lug of your arcade switches to your breakout box’s ground wire…don’t even run a wire to the switch’s pad.
Connect the other lug on your arcade switch to pin 2 (only pin 2) of the switch on the board.
When you are holding the board up, with the pots at the bottom, pin 2 is on the top right of S2 and S3. Pin 2 on S4 is the top left pin.
I hope that makes sense.
-Brach