oops david :-)
for the handle release issue, you want coin relay tripped like you show in your picture. The coin relay should be tripping or your coin accepted light wouldn't turn on. The below assumes the coin lockout is working so the game accepts coins when appropriate, but diverts them back out to the tray when the power is off.
got an ohmeter? it's handy to have alligator clip probes (or a jumper wire so you can clip a probe to a spot), as well as needle probes you can poke on wire solder joints.
If so, the circuit you care about starts are the blue/white wire on the leftmost switch blade(s) on the coin relay, so clip a meter probe on the bare wire connecting the two switch blades.
when the coin relay is tripped, you should see zero ohms on the white/red wire on the second switch blade. Either pull back the plastic insulator sleeve or poke the meter probe into the back of the sleeve far enough to touch the solder joint. You ideally don't want to probe the blades, but if you do, probe close to the stack to minimize the chance of the probe pushing the contacts together and making the connection work.
if you get zero ohms, wiggle the long blade a little and made sure reading stays a solid zero ohms.
next move the probe from white/red wire to the white/red wire on the C switches. The C switches are vertical and right above the coin relay switches. The white/red on C is the other end of the wire on the coin switch, so you better still see the same reading :-)
then move the probe from the white/red wire to the black/yellow wire on the C switch. Should still see zero ohms.
leave a probe on the blue/white wire and attach the other probe to the black/yellow wire on the handle release relay. Stick the reel mech back in with those probes connected and see if you get zero ohms.
this is where a continuity tester can lie to you. Once the reel mech is back in, there's other circuit paths thru coils possible. You want zero ohms ... or very close to zero. If you get a few ohms, you likely have a problem.
finally, move the probe from the black/yellow wire to the white/blue wire on the second blade from the top, again looking for almost zero ohms.
if you find a spot where the ohms value jumps up, you have a poor connection.
those are the three switches shown on the schem. You can skip any steps you like ... e.g. you can start with a probe on the blue/white wire on the coin relay and the other probe on the white/blue wire on the handle release relay.
another option is to probe the plug pins. The charts on the bottom left of the schem will show you where wires 25-1 and 83-1 are. Stick the probes there and you should see zero ohms when the coin relay is tripped. Manually reset the coin relay and you should get infinite ohms. If you do, the coin relay switch and reel C switch is probably fine, so that just leaves the plug connection and the handle release switch.
if you don't have an ohmeter but have a jumper wire, you can put one end on the blue/white wire and the other at whatever points along the circuit you want, stick the reels back in and see what the handle release does.
you probably dozed off by now, but if you don't find an issue, then it may be time to switch to voltmeter or jumpering wire 30 to points along the circuit and see when the handle release trips.
having said all that, most people just cause the switch stacks to operate by manually tripping/resetting the relays and watching the C stack during the reel spin. You'd look for switches that contacts barely touch each other and clean/adjust those for better switch action. If that doesn't fix the problem, then get the meter or jumper wire out.