With the machine off, pull the display and look at the large header pin solder joints on the back-side. Often a few of them are cracked or have cold solder joints. You can usually see the cracks in the solder around the pin itself. Years of dust/dirt might mean you have to brush the solder joints off quick with an old toothbrush to inspect better. Don't use the wife's toothbrush

Easiest thing to do then with a display with issues is throw it into another player position and see if it exhibits the same issue. Best to throw it in Player 1 position since the wiring from the MPU starts there. If it works fine, try a "working display" in the Player 4 position. If the working display has issues at Player 4 position then you're problem is likely at the Molex connector.

As far as connector issues, some used crimp terminals and some used IDC (wire pushes into the connector from the top). The terminals can fatigue over time, or they can get corroded. On the IDC style, the wire can sometimes work loose from where it pushes into the connector. If it's a connector issue you'll need to fix the bad wires or bad crimps to ultimately resolve things.