I've never had one of those apart, but they are still using 19 connections between the motherboard and the FPC (button) board, so they may be doing something similar with it.
On the official controllers, they use quite a messed up scheme for the buttons.
All of the face buttons, D-pad, Share, Options, /\, [ ], O, X, the TouchPad button and Reset button, are all active Lo, aka go to ground when pressed.
L1, R1, L3 and R3 are all active Hi, aka they go to 3.2v when pressed.
Now L2 and R2 are setup in a voltage divider circuit and each have their own common connections that are a PWM signal, 2L and 2R, and it's best to use those pairs, L2 and 2L, then R2 and 2R, if you are trying to make duplicate buttons, like installing Tact switches.
However, if you are attempting to make an arcade stick with that board, or some other project where only the motherboard is being used and you are removing the FPC board, you will need to install a couple of Resistors in there as well to keep half of the voltage divider circuit intact so that L2 and R2 will still work. Those Resistors are built into the FPC board, so if you remove it and don't fudge a couple of Resistors back onto the board to mimic the FPC board being there, then they will not work. You can see them on the FPC board in your pic, the one for L2 is just to the left of of the D-pad Up button, the one for R2 is right between the [ ] and /\ buttons.