Oswald's observable behavior was clearly desperate acts of avoiding contact, first of all when a Police car came along Jefferson, Oswald hid in the front of Johnny Brewer's shoe store
Clearly.

or he was looking at shoes.
and then next Oswald goes into a dark theater.
Or he was already there at 1:07 when Burroughs sold him popcorn and Brewer (who didn't see anyone enter a theater) misidentified him.