Since you have one working encoder (the other axis) and one dead encoder, you have a lot to work with. I'd focus on a board level repair. You've got only 3 parts on the board. Get an ohm meter and go around the board comparing resistances between the good and dead board. You need to test both polarities (reverse the test leads). That should let you figure out which part is bad. Get a photo of the dead part -- put it through a Google lens search. Note any numbers on it. Use terms like LED, photodiode, phototransistor. Companies like Mouser and Newark sell almost every electronic part ever made.
Also consider whether there is just a mechanical fault. There must be an encoder wheel, shaft, etc. this board reads. Something with black bits, or reflective bits. Make sure that part seems OK.
Edited by ngc7319_20, 02 April 2025 - 08:42 AM.