Yeah as you guessed, in 4:3 the mouse horizontal moving range doesn't match the 16:9 calibration, so the gun system needs to have a 4:3 content mode to compensate.
Doesn't the aimtrak have a this kind of mode?
If not, I think you will either have to play fullscreen or recalibrate every time.
The other solution I can think of is making mame using only 4:3 for the video zone but keeping 16:9 mouse range.
Not sure it's possible since it would require mame to process the black borders as part of the input video.