MADRID—Ignacio Buqueras is winning converts in his decade-old crusade to remove one of the last vestiges of Francisco Franco's dictatorship—the time of the day.

A punctilious entrepreneur, Mr. Buqueras says the bane of Spain is that its clocks are out of whack, dictating notoriously late hours that sap the country of efficiency and make it hard for anyone with a regular job to have time for much else.

After...