As the vehicles rolled, Mr. Hill heard an explosion from his right. He turned toward the sound. Kennedy was grabbing at his throat and lurching to the left.

Mr. Hill raced toward the vehicle — the heroic agent in now-iconic images from that day, climbing aboard Kennedy’s car.

Mr. Hill did not hear the second shot as he hustled to the first family. He heard, and felt, the third. Then he draped his body over the Kennedys. If a fourth shot came, Mr. Hill resolved, it would hit him instead.

“I wish I had been quicker,” he said Thursday.