I haven't owned STTNG for 5+ years so I'm unable to provide much new info. I did document how the mark and home should work on my site years ago. Maybe this is helpful? Specifically are BOTH mark and home registering correctly?

https://aaarpinball.com/STTNG/STTNG.htm

... Altan

I do know that the mark switch is not "somewhat irrelevant". The fact that your game is acting as if it is "somewhat irrelevant" is likely a tell-tail of the root problem. Unfortunately, I don't have the answer. I would suspect, however, you have inconsistent opto behavior. Some thougts:

Do you have mods that draw power from the opto voltage?

I'd try the "bang on the playfield" method. Go to diagnostics and bring up the switch diags that "ding" if any switches toggle. Watch closely for switches related to the cannon and pound your first on the playfield. Does anything quickly toggle?

If I was truly puzzled, I'd hook up a DMM that captures the lowest voltage seen and connect it to the mark switch's power. See if the voltage drops while the game misbehaves.

Good luck. Sorry I can only offer suggestions that might help identify the problem rather than pointing out the actual problem.

You've mention the mark switch, but can you confirm the home switch correctly detects home and detects when not at home?

When you power on the game, what does this cannon do? Does it swing the same way / times as the working cannon?