Can I use an action card after a unit has been gusted from the battlefield and there are no more units there?

Yes — the Showdown doesn't end when your unit is Gusted away. The combat/showdown only concludes when both players pass with Focus on an empty Chain, so after Gust resolves and the Chain empties, the state returns to Showdown Open and the player with Focus can play an Action (or Reaction) normally.

Two caveats:

• The action still has to be legal — if it targets "a unit at a battlefield" and you have none there, you can't play it; a spell like Ride the Wind (return a unit from hand to battlefield) works fine.
• You don't lose control of the battlefield while the Showdown is ongoing (Rule 187.4.c), so the battlefield remains a valid destination if you want to play a unit back to it.

This is the same principle as the Overzealous Fan ruling — removing a unit mid-Showdown doesn't close it, and control isn't lost while the Showdown is open there.