Given that CE163 was found in the TSBD and CE162 wasn't, it seems logical that the lighter jacket was the one Oswald put on @Beckley. Arriving in shirt sleeves nails it.
I just can't brush off Frazier's testimony. It's absolutely unequivocal. He is certain Oswald wore a light grey, long-sleeved zipper jacket that morning. There is no doubt about that.
Whaley describes him as wearing a jacket in his testimony as he does in this video [1:37]
In my mind Oswald is on the run at this point, he gets Whaley to drive past the rooming house so he can check the coast is clear and he double-times it back to the rooming house. The point of returning to the rooming house, as far as I can tell, is to pick up the revolver and get a change of clothes while he's there. He's in a big rush so I don't imagine it to be beyond the realms of possibility that he already had his jacket off as he entered the house. He rushes through the living room, gets the revolver (leaving the holster there), changes his shirt (making sure to take the transfer ticket with him), stuffs the revolver down his waistband and is putting his jacket back on as he rushes out of the house.
I originally posted the Brewer thing to Weidmann, not you, by the way. And did not find it 'strange' that he didn't see a jacket. Go back and try to figure out why I posted that to Weidmann, not you.
My bad about the Brewer thing.
I see what you're saying now.