Simple problem then, after all
"The Jamma to the Monitor" meaning the Jamma edge of the Tekken PCB to the first part of the Chassis (PCB that drives the monitor)? (The chassis is the big board, the neckboard being the little PCB attached to the pointy back end of the CRT itself, farthest from the flat side where the picture shows.)
Check the solder joints under and around the connectors of that grey cable at both ends. Even if they look ok you could reflow them. If it's not that, see if you can get a needle or pin into the ends of the connectors, to narrow the holes, so to speak, and help them hit the pins. If they still won't grip, you might have to redo the cable.
EDIT: looking at the pics more closely, there's a bit of room there to wiggle those wire individually, or at least watch what pulls on what when you move the cable.