Yep most likely 16sw opto board. I just had a very simular issue with my SS. Same board but it was a GLM 16 switch.
All the switches worked perfectly in switch test until you took one ball out of the trough. Then all the optos on one side of the board went bonkers. Switched out the board all better! STTNG and SS call for the same board. Marco has them.

Slow your roll. Before you go thru all the opto16 board testing, do me a favor and wiggle the connectors on the opto boards for the trough. I have had more then one STTNG that acted fine and every 5-10 games started loading and unloading balls, feeding more then one ball to the shooter lane, etc. it ended up being the 5v feed to the boards and no banging on the playfield didn't cause it. It ends up being an intermittent drop in voltage and then it the 5v comes back up. Redo the header if this is it and your golden. Easiest check it to grab the wires about 2 inches from the header and just wiggle a bit while in switch edge test with balls in. it will flicker like a strobe light while you wiggling and be perfectly fine after.

Also check that your inlane eddy sensors are properly adjusted. The game gets very confused if it "sees" the ball continuosly at eddy.

Definitely check the trough boards and connectors. I had to replace my trough boards several years ago with the great plains modular boards. I just recently had a weird opto problem where one of the optos would work intermittently. Replaced the faulty opto with no difference. Turned out is was the opto board where a cap had leaked all over the place. Sent it to Eugene Mosh and he fixed it up. I borrowed a 16 opto board out of a JY to test to make sure it wasn't something else.

Totally sounds like trough opto board issues. Probably just a loose connection or flickering emitter.

Trough always a problem on sttng. Make sure diverters aren't gummed up either. That'll cause staging issues later too.

I have had the exact same thing happen on my STNG and have not been able to fix yet. Besides the symptoms the OP states, my game also seems to randomly start modes or load a ball into the cannons....just strange behavior. I did as the Tallon suggested but didn't see any optos flicker on and off in switch test mode. My board connectors are not discolored either, so not sure it's the 5 volts. So the consensus then is to by new through boards?

I would suggest pulling and cleaning the subway and VUKs in your case. The optos in the subway and VUKs get very dirty and make it act very strange. Since your problem seems to be isolated to the subway area, I would start there. Also check the “stack” opto in the VUK. Dirty or cracked solder in the tiny board can make it read like there is a ball stuck in it and will feed the ball to the cannon to clear the problem

Guys, all the advice I give for this game is assuming you have already CLEANED everything including pulling EVERY opto and either cleaning with qtip and alcohol or pulled the bigger boards and took them to the sink for a good scrubbing. 90% of the problems with STTNG is dirt. Great game when it’s running. Crazy game to deal with when it’s not.

https://pinside.com/pinball/forum/topic/sttng-clean-up-for-mgc

One other thing with STTNG. Ribbon cables. When the ribbon cables go bad in this game the cannons do strange things.

Definitely sounds like an opto issue, possibly connection related but can also be:

... low +12VUR on PDB
... failing part on the 16 Opto board or trough boards.
... cracked solder joints on any of the boards mentioned above.

Side Note:
The ORIGINAL 16 opto boards and trough boards are 100% repairable, if you are looking to get these tested and repaired send me a PM, or if you decide to replace them and it fixes your problem PM me as well as I may be interested in obtaining your bad boards.

I had the same issue with my STNG. Ended up being a bad connector on the trough opto board. Repinned it with crimp pins instead of the IDC connector and its working like a charm again. Put it in switch test mode and wiggle the wires on the trough connectors and i bet you'll find your problem.

I've been fighting the game putting two balls in the shooter lane for a few days. Tested all optos successfully. Replaced the trough boards with a backup I had. I tried Chuckwebster's wiggling test and sure enough one connector was a little loose. Trimmed the wire back and reseated the connector. Played one game so far and it played great. Almost got to Final Frontier a second time! 3.6B. I'm going to keep testing to see if this fixes everything. I still might go back and reflow the opto wires.