usually all the wires on the door go thru the door plug (if they aren't just connecting things on the door).

plug chart on the schematic says a solid green wire is 40-5. Hunt around the schem for that and you'll find it around B14.

it's in a circuit that disconnected meters if the front or back door was open. The idea was you didn't want the meters to increment when the game was being serviced.

the switch itself would have been mounted vertically under your fingers in the pic - below is a picture of the Hawaii door.

if you don't have meters, it's not needed. If you do have meters, sometimes people just wired out the door switches to make it less likely for the meters to stop working.

int-hawaii-inside_coin_door (resized).jpg

p.s. don't compare stuff on the hawaii door to yours and think there's an issue. For example, the coin switch in the hawaii pic is a 2-terminal one. You have the more common 3-terminal with an unused terminal, which is fine.