One of my joysticks started to do this muted "click" when moving it up and down. It's really subtle, like you can very gently touch the end of the range by tapping the joystick shaft on the Deck's chassis, then you can push it a little more and it'll do a little "bump."
I took the back of my Deck off, unplugged the joystick, removed the three screws, and pulled it out. Then, I pulled the cap off and saw that the cap is just a friction fit on the shaft, and the cap is simply loose and wobbling.
To fix it, I cut a 1 cm x 1 cm square of plastic from a ziplock bag and put it on top of the shaft. Then, I squeezed it with my fingers to kinda form it to the shaft so it'd stay put. Finally, I pressed the cap back on.
That's it! The little piece of ziplock bag helps the cap grip the shaft and stay put. You can attach it back to the chassis with the three screws and reconnect the ribbon cable to test it with the back off just in case anything is wrong, then put the case back on when you're confident.
Also, the ribbon cable comes with a couple pinched folds, and is taped to a daughterboard PCB. It's easy to damage. Here's a part that's a near-exact replacement that works great, in case you break yours:
https://www.digikey.com/en/products/detail/molex/0150200097/2817187
