As John I said..
JED is Jack Edwin Dougherty.
Only one person fits the following, "the closest person without an alibi, with unimpeded access to the shooter's nest, whose testimony is unbelievable, had military training, and was "emotionally" unstable"
He reported being at the back of the 5th/6th floor, but is not seen by Bonnie Ray Williams (BRW) as he traverses from right next to the shooters nest to the front of the 5th, about 2 to 3 minutes before the shooting. Nor does he see Oswald flight.
Reports using the lift done to the first floor, but the conversation he claims he had with Eddie Piper, Piper can't remember.
His out of character action of returning to work early, his laughable reason for not watching the parade (clearly didn't remember windows existed).
If Oswald had have reported hearing a noise, travelled all the way to the first floor, been told that the President was shot, then went back to work by himself, LNers would take it as clear evidence that he was the shooter.
QED is Quod Erat Domenstrandum