Please let me tell what I see when I go to Add/ons
As I've asked in my previous message: are you STILL seeing all menus even AFTER you pressed CTRL+F12 at a parking and verified it doesn't do anything ? The reason why I asked this, is to be sure that GSX hasn't crashed when you are parked, which MIGHT indicate a problem with the airplane configuration.
Show GSX Menu by-passing YouControl M - I have tried several keys to avoid conflict
You should try the default key first, which is CTRL+Shift+F12. However, this should affect the other GSX key, which is the CTRL+F12
Your problem is not GSX, if you have another add-on that use CTRL+F12 but is activating its usage ONLY at the parking, you should find other free keys, assuming this other add-on can't redefine its own keys. I believe there's an online flying client that uses CTRL+F12 by default.
This is the most likely explanation with your described behavior, because everything in GSX seems to be working normally, if it wasn't working for some reason, you wouldn't see any of its menus.