Hi Vincent,
I have the exactly same problem. This piece was fallen off, while soldering out the Analog Sticks, without realizing that it was fallen off.
My Sticks are very smooth now, but I just have a problem in addition. Moving the left Analog Stick to the right and also in an angle of up to 90° up or down from this point, it also triggers L3, even its not pressed. The other, left side (up to 90° up or down) not.
As I realized, that this component is missing, I suspected, that this missing component is the problem. Now, I also have the problem, need to know what kind of component this is. I had a look in the schematics, and this should be a 100kOhm Resistor. I soldered one with some “flying cable” on it, but this was not the solution.
Any hints?