How many of them were behaving like they were avoiding the police in the aftermath of not one but two major crimes?
The sum total evidence that he was "avoiding the police": He looked funny and scared to Brewer.
More than that. Police cars are approaching Brewer's store from the East, sirens blazing. A somewhat disheveled That Man (again, hereafter TM) tucks into the vestibule at the store's entrance. He doesn't enter, but just stands there just outside the door and keeps his back turned to the street. Brewer notices that TM is staring (as you like to point out), but he's not staring at the merchandise in the store or the display cases on either side of the vestibule. The police cars make a U-turn at Zang, half a block short of reaching the shoe store, and head back to the East. TM looks over his shoulder, then proceeds in a Westerly direction, away from where the police cars came from. TM continues on until he reaches the Texas Theatre, when Brewer sees TM disappear into the recess at the front of the theater. Brewer walks to the theater, doesn't see the guy reappear, and notices TM isn't in front of the theater when Brewer gets there. Brewer realizes that TM had to have entered the theater, and asks the ticket clerk whether she'd sold TM a ticket. He gets a negative response; the guy snuck in. You might be the only sucker alive who couldn't see that as suspicious and evasive behavior.
How many snuck into a theater without buying a ticket? The latter, IIRC, is considered criminal trespass in Texas and is a class B misdemeanor. The police had Oswald just on that.
That would have been really hard for them to prove, given that nobody actually saw or remembered him entering the theater. And he wasn't arrested for criminal trespass, he was arrested for murder.
He was arrested after he struck a policeman and pulled a gun. Let me guess: you don't consider that suspicious behavior, either.
The criminal trespass thing would in itself have created probable cause to arrest and search Oswald once Brewer pointed him out.
However, we don't need to have a witness who actually saw TM enter the theater. Let me go over this again: Brewer saw TM walk to the theater and make a right into the recess at the front of the building. Brewer took off in that direction, didn't see TM reappear onto the sidewalk, and didn't see TM hanging out in the recess when Brewer got there. The
only place TM could have gone is into the theater. Postal testified that she saw TM enter the recess, but did not see him go past her when she turned to see what was going on West of the theater. Just based on her testimony, he could have turned around and headed back East, but Brewer's testimony rules that possibility out. And if Postal couldn't remember selling TM a ticket.....
And a good test of whether someone had bought a ticket is to see their ticket stub, BTW.
