Q: Since the air does the work, how thick does the air gap need to be?

A: The optimal air gap is about ½”. This is supported by both academic research and experiments I did on my own with small double-pane windows that I made in varying thicknesses.  Almost all double and triple-glazed windows use this spacing. If the spacing is larger the ½” the insulation value goes down because then convection currents start to move the heat from one side to the other.