My guess is you don't need to get the complete monitor out. These kind of problems often are in the PCB on the picture tube neck, not on the main PCB. Try to GENTLY tap to see what happens with the red gun. If so, try and see if you see any bad solderings (cracks/moving pin). If not, simply re-solder all the solder points (or do a couple, then test, if not fixed, do another couple, test again....etc.)
Also, I assume you are running the original arcade game (Ms.Pac Man). If not, if you're using a PC and MAME: check your VGA connector on your video-card ! Believe it or not, those screws on the connector are actualy meant to be used !

I've worked at a VGA monitor company, repairing them, and about 25% of the returned monitors were FINE, and always with the same complaint: blueish/greenish picture (=No red gun). The pin for the red signal is all the way on the edge of the VGA connector. Those people were too lazy to use the screws on the connector, and it wiggled out....but I may be getting WAY off now