gun games require a bit of TLC. the good news however is that once you get them running the way they should, they should be fine for awhile.
there's several tools and concepts that you need to know first... most notably about power supplies. ALL JAMMA based video games are powered by +5 volts, and depending on the age of the power supply, resistance across wiring, or simply the game board's power needs will all determine how you need to adjust the +5 setting on the power supply.
there's a +5 adjustment knob in most cases, others will require you to use a small phillips head screwdriver to turn the adjustment pot on the inside.
you will need a digital multimeter to determine what the +5 is set to. your power supply can come in any variety of form factor. the most common ones are the screw terminal types (all the necessary JAMMA power wiring are forked and screwed into lugs) or they'll be in a small computer power supply-like box with a molex connector with different colored wires going into a 9-pin plug.
the red wiring is for +5, yellow is for +12, black is for ground, and white is for -5. depending on the kind of game that's in your cabinet, you may or may not have or need -5. so to test, set your meter on a 20VDC range, put the red probe of your meter where the red +5V wire meets, and the black probe to where the black ground wire meets. you will then get a reading for what the +5 is set at.
to get the most accurate reading, you would do this at an IC on the game's board, but that might be a bit much to tackle all at once.
if the power supply is old, the components inside will break down some, and the unit will become less efficient, meaning that it won't output voltage as efficiently at the current +5 setting as it did before. if you're under 5 volts, like say 4.92 or something, that will definitely cause your gun tracking problem.
with your meter still attached so you get live readings, gradually turn the adjustment pot up (make note of which direction you have to turn it, it will be labeled) until you reach 5.15. then try calibrating the gun again and see if the tracking improves.
there's more...
if your monitor hasn't been cleaned in forever, the dirt on the screen will prevent the gun from tracking effectively. you will need to remove the monitor glass and clean both the glass and the monitor tube, preferably with Windex. additionally, if the monitor isn't set right (brightness is too low) it will also cause tracking issues. you want your brightness to be turned up high enough to where a black background is still pitch black... you don't want to be able to see the on-screen pixels in a black background.
if you find that the monitor is still too dark, or the colors are smearing, you're looking at a monitor issue that will require further diagnosis entirely separate from your gun issues.
I don't remember what size heads they are off hand, but you will need a security torx set to open up the guns. your gun that's completely dead may have something as simple as a broken wire or a connector that popped out of it on the inside. you'll never know until you look inside though.
I hope that gives you a good start of what to look for!