I have a Thrustmaster TCA Sidestick Airbus edition, and about a week ago I started experiencing these twitching false inputs on the rudder. It had a distinctive tendency to produce false inputs to the left.
I noticed that these twitches were more or less pronounced depending on whether I was applying pressure on the stick, and also whether I was pulling up or pressing down on the stick.
I could even see the intensity of the false inputs in the windows usb controller settings.
This indicates the issue came from the hardware and not the simulator.
I opened the stick handle by removing all 7 screws (5 outside on the left side, 2 inside the side buttons housing on the right side) using a Philips screwdriver, and found the source of the problem :
The wires coming down from the head of the unit were all tangled up together when passing in front of the Z-axis sensor (yaw sensor) and pressing hard on one of the contacts on top of the Z-axis sensor. There was also a pretty big glue filament linking the top of the Z-axis sensor and the rest of the handle, showing the unit was assembled quite hastily.
I used scissors to remove the glue filament and get a clean interior.
Then I untangled the wires and spaced them evenly inside the handle so that they would no longer put so much pressure on each other (especially near the Z-axis contacts on top of the sensor).
And here we go ! A fixed Joystick with clean and precise Z-axis, like new !