How do I fix the joysick’s x axis plastic that broke

I noticed a weird behaviour in my game, and in calibration i saw that the x axis of my jostick was working poorly, i took it apart, and found out how it works, (kinda similiar to the Z rotation sensor) and found that it broke. Now i’m a rookie in fixing stuff, but i cant really apply glue to either side of the plastic because, first it doesnt look like it would be long enough to work, and also because i have no way of holding them together until the glue sticks. If neither of these problems are valid, i could try somehow, but before i need a replacement i thought i’d look it up.

The way it works (or it looks like) is the cable pulls the sensor when the joystick is moved, and that little (broken) plastic ephasises the movement so that it can be detected properly. If it breaks, the cable kinda just hangs there, barely pulling on it, as seen in the video attached.