Yes this is correct. With the game off ohm out IJ19 1&2 and IJ20 1&2 to ground. If there is a dead short, the relay K1 is probably stuck closed mechanically. Then ohm out emitter to collector on Q67, if this is shorted then the relay is being pulled in by a failed Q67. There are other not so common causes, so if it is not either of those, then with the power on I would start by looking at the signal to Q67 to see if it is actually turning on and off when the game is told to start. If this doesn't change state, then the problem is likely upstream before Q67, if it does change state the Q67/downstream. Good luck.

When I power mine on while holding the relay I can definitely feel the click - it is small but it is there. But no short at J19 J20 to ground when the power off doesn't really support stuck relay contacts. The game on pulling in the contacts during attract mode would suggest something else is turning on K1.

I would recommend to back up and check the solenoid side first to be certain.

First use your DMM to measure resistance (game off) from the anode side of D3 to ground. You should get a slowly rising resistance from around 100-150 ohms that creeps upward.
Then with the game on measure DC voltage on the anode side of D3 (non band side) directly above the relay. You should have 5VDC there when the game is in attract mode, and should drop to nearly 0V when you press the start button. If you don't have 5VDC on the anode side of D3 the problem isn't the relay. If you do have the 5VDC at that point I would just replace the relay.

Probably U50, just shotgun replace if you feel lucky, but I would make sure the problem doesn't extend further upstream myself.

Correct, if the problem is isolated to the flippers in your case - if it doesn't bother you to not have the game work perfectly as intended and there are no other problems it is perfectly fine to leave it alone. In Papazit1963s case he has a few other issues that may or may not be related. U50 feeds some other circuits and could be related to other problems. I think it is a good idea to track it down and resolve it in his case.

Congrats! Nothing like a good game of F-14!