Here's the excerpt from The Kennedy Detail, pp264-265. I'm surprised this story hasn't gotten more attention:
Washington, DC
November 23, 1963
2:15 AM
Standing outside in the pitch-black darkness, Agent Jerry Blaine tried desperately not to yawn. He was on post at the rear corner of President Johnson's large two-story French chateau-style house close to the back door, and with the exception of the forty-five minute nap in Austin and some catnaps on flights, it had now been nearly sixty hours since he'd had any sleep. Blaine was almost to the point where he was hallucinating.
When he'd taken over from Andy Berger just before midnight, the two had simply looked at each other without saying anything. What could be said?
Blaine had been at this particular post for about fifteen minutes when he suddenly heard the sound of someone approaching from the clockwise direction. It wasn't rotation time, and he knew a Kennedy Detail agent would never approach from that direction.
Instinctively Blaine picked up the Thompson submachine gun and activated the bolt on top. The unmistakable sound was similar to racking a shotgun. He firmly pushed the stock into his shoulder, ready to fire. He'd expected the footsteps to retreat with the loud sound of the gun activating, but they kept coming closer. Blaine's heart pounded, his finger firmly on the trigger. Let me see your face, you bastard.
The next instant, there was a face to go with the footsteps.
The new President of the United States, Lyndon Baines Johnson, had just rounded the corner, and Blaine had the gun pointed directly at the man's chest. In the blackness of the night, Johnson's face went completely white.
A split second later, Blaine would have pulled the trigger.
President Johnson looked at Blaine, said nothing, and turned around and went back into the house.
Jesus Christ! I almost shot the new president. What the hell was he coming around the wrong way for?
With all the new security measures put into place that night, in the chaos nobody had thought to inform President Johnson about the standard counterclockwise movement protocol.
Blaine struggled to regain his composure as the reality of what had just happened washed over him. Fourteen hours after losing a president, the nation had come chillingly close to losing another one.