How does the sway control work in an Equal-i-zer hitch?

Something doesn't look right with your installation. The L-brackets should fit flush against the link plates. The nuts on the link plates should be on the inside.
The two 1/2" x 3-1/2" bolts should fit into the pocket on the outside of the link plate.
You might have the outside link plates backwards, I can't tell in your picture. That would cause the heads of the bolts to prevent the L-brackets from fitting flush.