you always want the header that's labeled "PLAYER 3". I reckon Midway did it with that weird naming convention because of all the 4 player games that they made, which of course the PLAYER 3 and PLAYER 4 each have their own harnesses for joystick and button inputs and they just wanted to follow the same format. so logically the next set of JAMMA+ inputs would be for "PLAYER 3".
note the orientation of the pins, I wanna say these headers have 15 pins, and they're marked 1:::::::::::::::15. you wanna match up the 1's, you might've plugged it in at the wrong end, which is why you only got one button to work.
(worthless trivia: UMK3, being a Wolf board which was shared with WrestleMania and NBA HangTime, also comes with a PLAYER 4 harness. Midway probably did this to consolidate everything into one board layout.)
an item to note, your Run and Low Kick button switches will need to be swapped. the KI2 button 6 = Run in UMK3.
I know all about these: they're practically the ONLY games I own. last year I had only 1 cabinet to play with for swapping all the MK and KI games in and out -- now I've got more "dedicated" configurations available to me.