Is this a GSX issue, or a FlyTampa YSSY issue? I'd really like a fix so I can get back to a more realistic pushback.
Of course it's a FlyTampa issue and not a GSX issue. They have the habit to always set all their pushback preferences to "None", most likely because FSX doesn't care and treat both "None" and "Both" as the same (FSX pushback always work).
However, it's very unlikely any airport would *always* allow Both direction at all places, there are always places were you cannot select a direction so, ideally, a scenery designer should always take the time to indicate such places in the AFCAD.
But that's not really a problem, you can do a quick fix using the "Customize airport positions" option in GSX, select the whole airport ( click the ICAO root node in the list on the left ) and set the Pushback preference to "Both", so you'll see Left/Right too, in addition to the "Straight Pushback" option, which is the only option available in the case the parking spot is set with a "None" Pushback preference in the AFCAD.