Put the game into solenoid test. Check to see if both the A and C sides are firing simultaneously. You may have a short across that relay, or only part of its shared circuitry. The solenoid tests should help narrow things down further.

During the solenoid auto test, #'s 1 thru 8 each have an "A" and a "C" side. Usually "A" is a flasher, and "C" is a solenoid. This corresponds to the chart in your manual, and you will see this scroll across the display as the test progresses. The A/C relay (which itself is #14) is supposed to only allow either the "A" or the "C" to operate. So when you watch the test, if you observe a flasher and solenoid operate at the same time, you'll know something is wrong.

I'm not familiar with F-14 directly, and I note some of your affected coils do not have A/C matrixing, so your issue might end up being a bit different. But solenoid test mode is the place to start. It's easier to isolate faults in test mode rather than the randomness of game mode where multiple things may be happening at once.

The A/C circuit itself gets a little more complex the deeper you go, but we'll save that for now. I once had an issue with my Space Station where A/C sides were going off simultaneously causing all sorts of madness... the tests helped narrow down the cause (ultimately, the A/C relay circuit was instrumental, but not the issue).