The back of your door is somewhat similar to my 1975 Williams Little Chief door, but not exactly. I'm in the middle of cleaning/refurbishiing mine so this is a bit sketchy, but here are some pictures that may help.
The first is the coin mech itself. Each mech has a pair of pins as shown here at the bottom:
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These will fit into the plate at the front side of your door as I try to indicate:
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Each mech also has a retaining plate on the side opposite the pins:
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This plate clips into the spring retainer clip just above the coin switch on your door:
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Note that my game did not have any coin mechs when I got it; I picked them up on Ebay. When they arrived the pins I show were on the other side, which was a bit confusing for a while. Also, they did not have the plates; I ordered from one of the pin suppliers (I'd have to dig through my notes/receipts to figure out which).
So basically the pins locate the mech on the door, and the plate/spring locks it into place. Hopefully this helps some; I've been a lurker on here for a long time and this is my first attempt to give back for all I've learned!