I go into the sim, choose and airport and open it, the GSX window comes up and I choose to configure my aircraft and so another window comes up but that window is in a hurry to leave and if it leaves you can do nothing. Click on the GSX logo all you want and nothing.
From your description of the problem, it seem your issue is just you are too quick to open the menu, and expect an immediate response. The first startup will be slow, because the airport cache must be recreated, and during this time you can't use GSX.
The menu you said "closed itself", was probably because *finally* completed loading and to prevent the menu to popup unwanted, as part of the start up, the menu will be closed in case is left open, but you opened it in the meantime, to the two open/close competed with each other.
Same when you say "no amount of clicking on the GSX logo will open anything". If you click too quickly without allowing to load, you are continuing to kill/restart the menu code.
This is a way of the way of the interaction between the Html/JS system and Simconnect and WASM interact and the fact the toolbar menu code is automatically killed ( whatever you were doing ) by the simulator itself in the very moment you close the toolbar icon so, you click again it must go again to some restart procedure.
First opening on a gate can take 3-4 seconds, because it's searching for vehicles to load, it's creating traffic cones and the underground refueling hole and it's looking on SimBrief in case you have a flight plan ready for this airport.
Just go slower, and it will all works.