Half a millennium ago, in 1513, the Spanish explorer Juan Ponce de León departed Puerto Rico for the verdant island of “Bimini”—an uncharted land in what is now the Bahamas. He eventually landed instead in Florida, where he staked a claim for the Spanish Crown and ensured himself a spot in the annals of history.

As legend has it , and as scholars have maintained for centuries, Ponce was in search of the Fountain of Youth, a fabled wellspring thought to give everlasting life to whoever bathed in or drank from it. But new scholarship contradicts the old fable and suggests that Ponce was interested not in longevity but political gain.

The real story goes something like this: In 1511, messy political squabbling forced Ponce to surrender the governorship of Puerto Rico, an appointment he had held since 1509. As a consolation prize, King Ferdinand offered him Bimini, assuming the stalwart conquistador could finance an expedition and actually find it....