It is important to note that Cooper later on realized that …

It is important to note that Cooper later on realized that we was given documents on purpose in order to leak false information.

Shortly after that realization he was killed. Before that he was allowed to leak all kinds of stuff.

Any high resolution copy of the Zapruder film shows very clearly that the driver didn't have a gun. It really is a reflection.

And if that isn't convincing enough, try shooting and hitting from that position. With your left hand.