Bought faulty - only the thumb sticks and start/select worked. I figured there was a broken trace in there somewhere and something that would be simple to fix.

Or perhaps a build up of carbon on the silicon pads that "just" needed cleaning.

It turns out that these controllers, instead of bridging the pad when the buttons are pressed, use a resistor (the dark rectangles) that when pressed, the resistance increases (or decreases…though I'm fairly sure increases) and that is measured.

The problem is that over time, as they're pressed more and more, the resistance naturally builds up as the resistor fails under the physical pressure and eventually it can't tell when the button is depressed.

The only solution is to buy an entirely new membrane (seen in the photo). But now it works!