I have pushed both AA and CX a lot to assign a seat on an AA*CX flight from HKG to LAX without any success (as OWE). I think the system is hard-coded to disallow seat selections on all Economy codeshare flights. Since BKK to HKG is somewhat short, and the fact that the CX seating assignment module (Amadeus "Theoretical Seating"?) does tend to assign elites pretty reasonable seats, I would not spend hours fighting for that seat assignment. This could be due to the Econ Light Fare family change, or it could be a remnant of the COVID-era seating policies that never got fixed.

If you do decide to call and asking for a specific seat doesn't go anywhere, try to ask the agent if you can indicate your seating preference. If the agent has native Amadeus it should be a different command that doesn't involve the agent pulling up a seat map that is full of blocked seats. I have never tried that but figured it might be worthwhile to try