Next was to simply push the correct terminal into the housing - in the right order. 

From the schematics the order is as follows for J3:

Pin 1 - 6.3v AC
Pin 2 - 6.3v AC
Pin 3 - switch ground
Pin 4 - Left Coin 1
Pin 5 - Centre Coin 2
Pin 6 - Right Coin 3
Pin 7 - Dig sw 1 (esc)
Pin 8 - Dig sw 2 ( - )
Pin 9 - Dig sw 3 ( + )
Pin 10 - KEY
Pin 11 - Dig sw 4 ( ent )
Pin 12 - Col. 2
Pin 13 - Row. 1