D'oh
I can save you some time and trouble, Mr O'Meara, by telling you where this line of inquiry will lead:
Either! Prayer Man is Mr Oswald, a quiet nondescript employee amongst a bunch of other employees, who told Captain Fritz that he "went outside to watch P. parade" and naturally enought went unnoticed by most of his fellow employees in the short time he was out there (though
not unnoticed by Officer Baker, Mr Truly and Mr Lovelady)
Or! Prayer Man is a non-employee of the Depository alone amongst a bunch of employees, who went weirdly unnoticed by every single one of them.
Seems to me option 'Or' is a much bigger stretch than option 'Either'!
Alternatively----------can you find another, hitherto unmentioned Depository employee to put out on those steps in the Prayer Man spot?