Technically speaking your wiring looks fine to that switch (pending continuity check on wire of course) so I’d start moving back to the board and check the wire associated in the molex connector and any cold soldering joint to those pins on the board.
Now on to the medium ramble for other visitors:
More often than not, a reflow of ALL header pins on EVERY board is a good habit to get into when purchasing these old solid states.
(New caps don’t hurt either.)
I’m guessing your game doesn’t desertT1 due to the free play comment but, if it also has the old battery still attached, clip it off, neutralize any acid that might have leaked and inspect board for any further damage due to the dead battery.
1. a SuperCap memory capacitor rated at 1 or 1.5 Farads.
Not so cheap.
2. The 5101 NVRAM replacement that Rob Anthony sells here: http://www.lockwhenlit.com/products.htm
I’ve also seen some .100 connectors where each hole was completely filled with aqua green “goop” due to the expired battery.
Not too good when you’re trying to make a solid electrical connection.
Hope that helps.