And to compound the problem of BRW and a 6th floor shooter missing each other in this 12:21- 12:23 time frame,leaving and entering the SE window by each party, is the supposed presence of Jack Dougherty on BOTH the 5th floor and the 6th floor during the same period of time.
This is a very difficult logistical tangle to work out.
Add in a possible revelation that Sarah Staunton (per interview with relatives), may be a 2nd witness to Oswald on the 2nd floor with a coke near or at the 2nd floor lunchroom , and since Staunton goes out to join BW Frazier, Lovelady on the front entrance steps, BEFORE Carolyn Arnold did, the time approaches ever closer to be nearly RIGHT AT 12:15 of Oswald being seen in the lunchroom.
So either Oswald was really seen in the 2nd floor lunchroom so close to 12:15, thats it nearly simultaneous with Arnold Rowlands SW window shooter observation timestamp of 12:15,, OR, Oswald went up and down TWICE to the 6th floor after being seen by Sarah Staunton about 12:13, then Staunton leaves, and then at 12:17, Oswald is seen by Carolyn Arnold, having returned again to the lunchroom from 6th floor.
And Oswald has to do this trekking up and down the staircases, while BRW is still on the 6th floor, and while Jack Dougherty is still supposedly working "getting stock" on both 6th and 5th floors, without being seen or heard by BRW or Jack Dougherty.
And Oswald also has to time precisely when to return to 6th floor just before Normand and Jarman, which would be just 1 or 2 minutes after having meet Carolyn Arnold at 12:17, and Oswald able to get past Jack Dougherty AGAIN for about the THIRD time.
Imo, there are only 2 probable places that Oswald could have hidden during upon returning a THIRD time to the 6th floor.
1. The 6th to 7th floor staircase, going "up" and at the midlanding, Oswalc would be generally out of sight, but still have probabilty to hear elevators in operation. Oswald is position to at least hear the elevator. Also Oswald is in proximity to hear voices, so he could have heard Norman and Jarmans voices on the 5th floor elevator possibly, as they exited the elevator on the 5th floor.
2. Oswald actually hid himself ON the 6th floor, having ability to see thru some crack in stack of boxes but was hidden from view of BRW. IF Oswald is in fact the gunman Arnold Rowland saw, then Oswald IS aware beforehand on returning to the 6th floor after being seen by Carolyn Arnold about 12:17, that BRW is probably STILL on the floor, and Oswald chooses a place to hide that will facilitate being able to see when BRW leaves.
How Oswald avoids being seen by Jack Dougherty is another question though, and it may require a propositon that Jack was actually taking a nap somewhere instead of actually working, and was in a corner asleep during all this movement of 4 persons using elevators amd staorcase. and walking across both 6th and 5th floors, yet unseen and unheard by JD.