Prayerperson looks to be taking a photograph. Oswald was an avid photographer. It really surprises me that he wouldn't try to capture the moment.
There's a nice moment related to that in Gary Mack's interview of Buell Frazier.
First let me tell you one of Vince Bugliosi's favorite courtroom jokes(told in his virtual prosecution of OJ);
Man takes his neighbor to court because his dog bit him.
In the dock the neighbor gives his defence,
"My dog is always in my yard, nowhere else
and he's always on a leesh,
he's never bit ayone in his life and besides, he doesn't even have any teeth and lastly,
I don't even own a dog."
Frasier went a similar route when Gary asked him did he think of taking a photo of the parade.
"I didn't know the parade was coming past the bulding" he said,
"neither did I know we'd be given time of to watch it
and besides... I didn't even own a camera".
True story.