your issue is the ball index relay is unpowering when it shouldn't. If you jumper the middle blade of 3E to the top blade and still have the problem, then it's not 3E.
- ball index relay switch A ... you can clean/adjust it or jumper it.
- outhole relay switch F ... you can clean/adjust it or jumper it. It's also a make-break switch. You want to check the middle blade going to the blade it touches when the outhole relay is unpowered - the top blade. However, if jumpering middle to top makes things work, you don't know if the switch is not working well or the outhole relay is powering at the wrong time and opening the switch.
tmi about previous posts
it'll make more sense if you can figure out the below stuff:
1] switch 3E is a make-break switch. It has three blades - long one in middle, and short ones above and below. All three blades in the purple circle are switch 3E, but the middle blade is only touching one surrounding blade when the stack is not moving.
2] with the cams lifting stack 3 as shown in picture, the long blade of 3E should be connecting to/pushing up the blade above it
3] circled in green is another make-break switch on the index cam. On this picture, the long middle blade is connecting to the short blade below it
4] since stack 3 is lifted, the contacts on the long middle blade and short blade beneath it should not be touching. The lower half of switch 3E in your yellow circle is correctly open.
cam stacks (resized).jpg
the difference between  and  is whether the switch stack is in a cam notch (red arrow) or lifted up on the cam edge (blue arrow)
to really see what's going on, with the game power off you can usually grab the cams and rotate them in the direction of the yellow arrow and watch what the switches do.
generally, you don't adjust the long blades unless they are floating in space when the switch stack is down.
when a switch stack is on a low point on a cam, all the long blades should be down and connected to the cam follower at the bottom via the white cylinder spacers. On your game, the cam follower is the plastic piece riding the cam edge.
anyway, you almost always want to adjust the short blades. In the case of 3E with game power off:
1] manually turn the cams until switch stack 3 is down in a cam notch.
2] verify all the long blades are down with no gaps between the white cylinder lifters. The long blade of 3E should be down as far as it can go
3] adjust the short blade on the top of 3E so there's a gap around the same size as the gap in the green circle. A little less is ok.
4] rotate the cams some more and watch what happens when stack 3 lifts out of the notch. You want to see the contacts close on the top blade BEFORE the stack is all the way lifted, and the short top blade should get pushed up by the long blade a little as the stack reaches the top of it's travel.
way too much bonus tmi
eventually you reach a point where you have to either shotgun things - check/clean/adjust everything in the circuit it could possibly be - or you need to unplug the score motor and turn the cams by hand with the game power on so you can see what the relays and steppers are doing in sequence. The one gotcha is you can't slow-turn or stop turning the cams if the 120V bank reset coil is powered or the fuse for that coil will blow. That isn't a concern if you aren't hand-turning the cams during reset.
in other words:
1] reset game
2] shoot and grab the ball
3] score 10/100/1000 pts so the ball index relay powers
4] tip up playfield without tilting game
5] pull out the score motor plug
6] manually reset the bonus unit so that's not complicating what happens next
7] turn the score motor cams by hand for a first 180 degrees.
when cam 6 switches fall in the notch, the outhole relay should power and stay powered. The bonus unit step-up coils powers. It may hum/buzz because it doesn't like being powered for a long time, but it can survive a couple minutes without burning up.
keep turning the cams and the cam 6 stack climbs out of the notch and the bonus unit steps up to light 1000. You'll get to the end of 180 degrees of rotation shortly after that. The end is when the index cam switches fall into the cam notch.
the ball index relay should stay powered the whole time.
keep going with the cam turning for another 180 degrees.
- when the cam 1 stack goes down/up the cam notch, the ball count should increment
- when the cam 2 stack goes down/up the cam notch, the player should increment
- when the cam 3 stack goes down/up the notch, the ball index relay should lose power
- when the cam 4 stack goes down/up the notch, the ball release coil fires
- when the cam 5 stack goes down/up the notch, the outhole relay should unpower
other stuff will happen during the above also.
if you really don't like fiddling around in the game with the power on, it's theoretically possible to mount a video camera in a spot where you can see the score motor switches (at an angle you can tell when they go up/down), the outhole relay, the ball index relay and the ball count unit at the same time. Video what happens and then watch it in slo-motion to see when the ball index relay loses power.
if the problem is intermittent tho, you pretty much have to use the shotgun. e.g. if a switch is flaky, the ball index relay could unpower at any time and you don't know which switch caused it.
if the above ever makes sense and you can derive the same thing (assuming I got it right) just from looking at the schem and cam timing diagrams, you'll be able to find problems in pretty much any EM game. Even a bally bingo can't baffle ya for more than a few cocktails.