First, be sure you disabled the GSX Jetway replacement files for that 3rd party airport, which you are supposed to do, as explained in the GSX Manual, Page 7
If you sure GSX jetways are not in use, GSX doesn't have ANY control over if a jetway works or not. GSX doesn't move, control or affect jetways, it only sends a command to the sim to toggle the jetway but, whether it would work or not, it depends only by your parking positions in relationship to the jetway, the airplane used, and the jetway model itself.