In this video of the wallet at the Tippit crime scene, the cop with the wallet is randomly waving his gun around, and without a care, even has it aimed close to the hand of the detective who is pointing something out within the wallet and then when the cop hands over the wallet, he quickly points the gun away and more towards himself.
The most likely scenario is that the wallet was being looked at legitimately and also as a bit of a show for the TV camera and thus the cop is a bit flippant with the direction of his gun, but when the civilian approaches and is given his wallet back, the cop responds correctly by diverting the aim of the gun and away from the direction of this civilian.

BTW, I posted this theory on the old Forum and Gary Mack who became a wise wizard, sent me a PM endorsing my theory.
JohnM