Screw the stick to a small peice of wood, and attach that piece of wood to the interior wall.
Drill a hole in a small wood block, run a screw through the block into the stick, then attach the block to the wall, You would only attach it to the wooden wall of the inclosure.
For the glass side use some double sided foam tape, or go for broke and get some 3M VHB tape (its like double sided super glue tape, but its expensive)
do the same with the other stick, cut the end at an angle and screw it together.
You could maybe use a piece of heavy slate floor tile, and just sit it there also.