I checked with my Galaxian. Everything is still original there. Assuming the first picture is showing the connector coming from the harness, the wires that are diagonaly opposite each other are the coin wires. When you short them temporary, you should get a credit. You can easily see which wires I mean, because on of the top corners is not wired.
On my cab the wire colors are orange/black and the other (double wired) red. You can wire both coin switches in parallel, that's how it is on my cab, although I only have 1 coin mech (the other wires are cut off and isolated).
If you look at the connector that is coming from the harness it should like this:
orange/black------ D-O ------ not wired
green/white------ O-D ------ yellow/green = ground
blue/brown-------- D-O ------ Red
Blue/Brown and Green/White go to the coin counter so DO NOT connect these to the coin switches. There's a electric pulse for every payed game on these wires.....
I hope this is clear enough. The Red wires on your connector look to be brown instead of red.....
If it's not clear, make a close-up (macro !) picture of the connector and wires...
And yes the yellow/green wire needs to be connected to the metal part of the coin door (at the point where that loose green wire now is on your last picture). This is for protection, if there would be an electrical defect inside the cab, a mains voltage could be going to the coin door....you can imagine what happens if you insert a coin should this happen (athough it's not very likely that it does happen).