I had a similar issue with the z axis on the tm16000 joystick for rudder input. Found the internals had become worn enough to supply input without touching them. The TM16000/TWCS series is known for wearing faster than something like an X52 and having this issue, I bought a new one online for like $50usd and it fixed my issue.
If money is an issue you can try calibrating or increasing the deadzone in axis tune. May get lucky, I didnt....When these are done for I'll be going back to saitek they just last so much longer for the same price range I've had an x52 last 9 years of constant use before any issues, TM ive had for 1 before problems started.