Anyone minded to dismiss out of hand the importance of the sizeable object being waved ('So somebody's waving something, big deal...') ought to consider the fact that it goes BEHIND the black man standing by the white west column but IN FRONT OF the man standing directly behind that black man:

This localizes the object nicely.
Somebody must be waving this object, right? And that somebody must be behind the black man, right?
Well, there are only two possible candidates:
1. The white man (=Mr. Lee Oswald) standing right behind the black man
2. The owner of this leg:

But who can the owner of that leg be?
The only two remotely viable candidates are
------------the man in blue (= Mr. Bill Shelley) seen back on the landing in Hughes

OR
-------------the owner of the red clothing (=Mr. Billy Lovelady, yellow arrow below) seen leaning over, and momentarily blocking the man in blue, in Hughes:


But we can rule out the man in blue on the landing (Mr. Bill Shelley) as the man waving the object because
a) he is too far back on the landing: he simply doesn't have time, in the less than two seconds between the end of the above Hughes GIF and the start of the Towner GIF, to come forward on the landing and step down far enough to be the holder of the object
b) Ms. Towner's angle--------more acute than Mr. Hughes'----------rules him out.
So it comes down to two candidates: Mr. Billy Lovelady vs. Mr. Oswald.
But we can rule out Mr. Lovelady, as Bell is just instants away from showing him like this:

Does this look like a man waving something back and forth? And did Mr. Lovelady say anything about waving something at the P. Parade?
So-----------the person waving the sizeable object must be the man in the reddish shirt standing right behind the black man by the white west column, i.e. it must be Mr. Oswald.
Now again, ask yourself: If Mr. Oswald were to wave something at a P. Parade, what might he be likely to wave?
