https://www.marcospecialties.com/pinball-parts/5791-10930-02 is the connector that goes into it although I forget which side is male. It's a .093 connector though not the .156's someone has hacked into your picture.

https://www.greatplainselectronics.com/proddetail.asp?prod=09-18-5061

is what it looks like but in a 2 pin version. (See the similar ones on your board to the left, 6 pin and 12 pin versions) Likely extremely hard to find as it's just discontinued. I would put the proper connector on the wiring from the game, and make up a pigtail connector with the corresponding plug and solder it directly to the PCB, that way if you ever do get the correct connector, you don't have to modify the game's wiring to swap it in.

No idea on the system 9 supply being the same, I don't see why it would be different, if the plugs are all the same, look at the schematic and see if the outputs are all the same. (position/type). If they are the same no reason you can't just use it in there (the 50v add on is always a separate board for the flipper power supply on later system 7's and system 9's, even into early system 11's)

Should have a Molex # 15-31-1026 on your board.

Great Plains has it:

https://www.greatplainselectronics.com/products.asp?cat=153