Why you donĀ“t connect to the same board ?
Not necessary new wires to the board, you only need to connect one button to another button connect already to the board. In this form, press one of the two button is the same task.
I have this in one arcade build, for buttons on the left and the right side for both players (left hand or right hand)
For you, you just add two button for pinball, you need to connect this two button with another two button from player 1. Is is easy.. no need to program anything.