I have a new theory. The last photo at your link says an entry wound through the throat.
Therefore I say that Connelly concealed a gun under his arm and shot backwards up into the throat of the President, because he either didn't like assh@les from Massachusetts or wanted another Texan to be president. Then shot himself in the elbow or whatever he got shot in to provide a coverup. The SS agent, running to the back of the car, thought he heard shots coming from the car, and figured Jackie had shot John for screwing Marilyn.