Yes, those photos are hard on the old eyes. But I can tell you these things:
First, yes, you are missing a nylon spacer in between those two zero position switches. The two blades should not be allowed to electrically touch. Both should normally be closed everywhere except 0 when they both should open. But this is only related to allowing the game to start, not for the specials scoring a replay.
Second, see that rather thick phenolic spacer (brown thing sandwiched in the switch stack)? That use to be a much longer piece that is also used as a spacer as well as a stop to prevent the other switches in the stack from coming in contact as well as stopping the ratchet from going more zero or too far the other way. Neither is really a big deal as there is a missing tooth in the ratchet wheel to stop it at zero.
As to the lower EOS switches. Seeing two, I can tell you that one of them (probably the top one with the larger point contact) is for energizing the Knocker coil (all the time except when coins are dropped). The other is that On Replay unit switch we keep refering to. This one should be normally closed and the contacts should open at the end of travel for the step up ratchet armature. This is what "breaks" the hold circuit to the EX relay and would normally cause the machine gun effect if the EX relay coil were actually energizing.
Sadly, you have one of those games with almost all "peach and tan" colored wiring due to age and the elements. This makes it rather hard to trouble shoot unless you know the actual color and can say, yes, that looks like it might be yellow/brown etc.
If you can, get one more photo of the wires going to the actual EX relay coil (not the switch stack). Try to get your camera to focus on the coil lugs, not the surrounding areas. I know it can be hard but see if you can get a good shot.
Since the EX relay is in the head, and so is the Replay 15th pos switch, we know that the blue/black wire merely connects from one to the other. The other wire to the 15th pos sw is Yel/Red and it should wind up at a normal open switch on the EX relay and then continue over to a jones plug to go to the Playfield were AX is mounted. From AX, we have that Yellow wire which in my game was actually a cotton wire and not a smooth plastic insulated jumper. It goes over to the A relay next to it and then, is probably jumpered to a second set of contacts on the A relay. This is the feed from the targets to energize the EX relay when AX is energized (specials lit).
The EOS switch blades should be insulated on that bottom double switch stack (this includes the actual metal blade not coming into direct contact with the stepper arm), connecting the Blue Black wire at EX to any Red/White wire in the head should cause the EX relay to energize and therefore advance a credit. It should not blow a fuse. You may need to unscrew the zero and 15th position switch stack and let them dangle so nothing is touching (including the solder lugs or other blades). If it does blow the fuse, we need to locate the yellow/red wire as it leaves the head (jones plug) and goes down to the playfield. Sometimes, its something like a nut or washer wedged in under a jones plug near the solder lugs shorting to an adjoining lug.
Meanwhile, when I get home tonight, I will try to get some photos off of my Hot Shot head. It too has wiring that is pretty dirty and weather damaged but at least, it might show us how the switch stacks are supposed to look so you can go from there.