Bill Brown, what do you think?
Gerry, first... In my opinion, we have to put ourselves in Oswald's position.
Regarding Brewer and Archer sitting in the pickup truck eating their lunch, if I am Oswald, I would walk behind the truck instead of in front if it simply because I want my face to be seen by as few people as possible. He has no idea by this point if his face was on the news as a person of interest. We know it wasn't, but he couldn't know that. It is roughly 40 to 45 minutes after the assassination and he left his rifle behind and has left work.
Consider the theory that Oswald had the library and/or the bus stop outside the library in mind as his destination when he left the rooming house. The library would be a great place (perhaps?) to lay low for a few hours and the bus stop outside the library could get him to the VA hospital further south in Oak Cliff where he could then catch a Greyhound to Laredo and the border. Upon reaching the location of Tenth and Lansing (where Tenth Street makes it's drastic 45 degree curve) and heading toward the library/bus stop, Oswald sees a law enforcement vehicle further to the east on Tenth. He doesn't see this vehicle until he is at the curve at the intersection of Tenth & Lansing, since the curve prevented seeing anything to the east along Tenth until actually at the curve itself.
Not wanting to walk past a law enforcement vehicle to the east of his location (has his face and/or name been plastered all over television?), he instead walks west on Tenth toward the eventual encounter with Tippit.
Oswald was quick to gun down Tippit. Why react so hastily? Myers theorizes that Oswald, walking west on Tenth, sees the approaching patrol car and does an about face. To me, this would make sense. Once again, Oswald, having no idea whether or not his face has been plastered all over television, turns around so that the approaching officer doesn't see his face.
We know that Unit 109 (Dallas County Sheriff Deputy) reported from the area of Tenth and Jefferson/Marsalis shortly after T.F. Bowley reported the Tippit shooting on the police car radio. If 109 was at that location shortly after the Tippit shooting, maybe he was there shortly before? Now having turned around and walking away from Unit 109 and then very soon after seeing Tippit approaching, a paranoid Oswald must have felt they were onto him. He guns down Tippit for this reason.
Here's my point (speculation alert)...
Oswald, on his way to the area of the library, does not want to walk past the law enforcement vehicle in the vicinity of Tenth and Marsalis/Jefferson because he doesn't want the officer inside the vehicle to see his face.
Oswald does not want Tippit to see his face so he turns around once he sees Tippit approaching.
Oswald sneaks past Julia Postal because he has no idea if she has seen his face on television and/or doesn't want her to later see his face on television and recognize him as a man she sold a ticket to earlier.
It is the same "consciousness of guilt" which causes Oswald to walk behind the Brewer/Archer pickup truck because he doesn't want the fellows inside the truck to see his face.