Assuming you have some method to assign keystrokes to a programmable physical button, which I guess is to be assumed if you are building a cockpit, why not just using that one to program a macro that emits the following keys in sequence ?
- CTRL+Shift+F12 ( calls GSX directly, bypassing the YouControl menu, if there is one )
- 5 ( select GSX Pushback option )
- 1 ( select first option, which is usually Left )
You can of course create a similar macro with CTRL+Shift+F12, then 5, then 2, for a Pushback Right, and assign it to another button, if you want.
Note that, if the scenery defines a parking with pushback allowed only in *one* direction, GSX won't wait for the "1" or "2" keys, and will just use that one so, the last key press will be sent anyway but not be read by GSX, but by FSX itself. It shouldn't be a problem, as long as it not used for something else by FSX or by another FSX add-on.
If this could be a problem, you might program just one macro with CTRL+Shift+F12 and then 5, and then choose Left/Right from the GSX menu, if there's one (depending on the parking spot)