the trip bank is the thing you are looking at on the bottom board in the cabinet. When a trip relay coil is powered, the switch lifter plate flops down and the relay is "tripped".
the only way to reset a trip relay is to physically raise the lifter plate so the coil armature grabs it and holds it up. Normally the white reset cams do that, but you can do it with your finger also.
to manually trip a trip relay, you poke something convenient like a wood meat skewer between the lifter plate and the reset cam and push left. That pushes the armature against the coil top, which trips the relay. You can also do whatever is needed on the game to get the coil to power and trip the thing for you.
there should be a paper label next to the trip bank saying what each position is. Usually there's two switch stacks on each relay.
I didn't notice the flipper plug. What they really mean is flipper button plug. It's one of the plugs on the front of the bottom board ... probably the left one. They did that so the bottom board can be removed relatively easily without unsoldering anything ... which you may need to do to get to the trip relay switch wiring without hiring a contortionist.
there isn't anything on the flipper plug that should matter, so you're looking for a short.
assuming you don't find anything, what I'd do is stick paper between contacts on one of the special trip relays and trip it. Pull out the paper one at a time to figure out which switch is causing the problem, then look at the wire colors on the switch.
you can also try and stick paper between closed switches after the relay is tripped or use something to open the switch ... but it can be tight in there so it's often easier to use small strips of paper hanging out, trip the relay so the paper is keeping switches open, then pull out the paper one at a time.
another thing you can do is pull out the plugs going to the playfield one at a time and see what happens. Most people pull the plugs with power off That will narrow things down a bit if you isolate the issue to one plug. If pulling the plug with wire 75-4 on it makes the flipper not power, I'd leave the plug out and use a voltmeter between wires 10 (or 80) and 75-4 on the socket. If you see 50V when a special relay is tripped, the issue is on the bottom board.
the 7 and 8 lights are a switch on the associated trip relay, so you'll need to check those trip relays. if neither the target nor the score lights work for the 7 and 8, take a hard look at the yellow wire on the center switch blade and follow to the adjacent trip relays. If it's busted or a solder joint is bad, all the "downstream" stuff won't work, and it's possible to get really odd behavior ... like your flipper issue.