On Nov. 18, 1963, in the midst of a whirlwind campaign trip, President John F. Kennedy told Secret Service supervisor Floyd Boring that agents riding on special boards installed near the trunk of his car should drop back and tail him from a follow-up vehicle instead. “It’s excessive, Floyd. And it’s giving the wrong impression to people,” said Kennedy. “We’ve got an election coming up. The whole point is for me to be accessible to the people.” Kennedy’s bristling at the proximity of the agents was not uncommon for those being protected by the Secret Service, especially US presidents. But...