Imo, Oswald’s reason to speak to Piper at 12pm was to inform Piper that Oswald was going “out” . This in order that should Truly direct PIper to go find Oswald , would spare Piper wasting time searching floors and would inform Truly that Oswald was unavailable , having left the building
It would be unnecessary for Oswald to inform Piper of “going back up” , since Piper’s job is mainly to find employees Inside the building as directed by Truly. Piper, unless informed of departure from the building by an employee, would thus naturally search the floors on presumption the employee was still in the building.
If the “going out” statement is more probable one made by Oswald, then the reason Is likely to get his lunch either from inside the paper bag package Oswald put somewhere in the annex roofed part of loading dock or to go buy some lunch
Either way, between 12:01 ans 12:14, Oswald is not seen on the 1st floor.
At 12:15 approx , Oswald is seen sitting in the 2nd floor lunchroom
By Carolyn Arnold
This suggests the following speculative timeline
12:01 Oswald has left TSBD to go “out” possibly to buy his lunch. The temperature is about 65 with wind gust up to 15mph , so if Oswald was acclimated to Texas 90 degree plus temperature , wearing his brown shirt and jacket to go outside is reasonably probable
12:10 Oswald is returning to TSBD with his lunch and from
some distance away, sees James Jarman and Harold Norman exiting back door of TSBD dock as they go around the NE corner of TSBD. They do not see Oswald however, as they are facing SE heading along Houston st.
12:12, Oswald enters TSBD and ascends to 2nd floor landing to check if the 2nd floor lunchroom is clear. He may have been seen by Sarah Stanton at this time carrying a Dr. Pepper ( vaguely remembered by a relative of Sarah as a “Pepsi”) Oswald therefore went up the staircase to 3rd floor, waited a few more minutes , then came back down and saw the 2nd floor lunchroom clear
12:14 Oswald sits down at a table in the 2nd floor lunch room, and takes off both his jacket and brown shirt together , leaving shirt sleeves inside the jacket sleeves, as is very easy for slender person with oversize jacket and shirt to do. Jacket and shirt left therefore hanging on the back of the chair.
12:15 Oswald seen sitting in the 2nd floor lunchroom , by Carolyn Arnold