Clocks roll back an hour this Sunday — to the chagrin of many Americans. But as the time changes, why daylight saving time started — and who was behind the effort — remain complicated.

“For watchmakers, clocks are now a way to peacock and create an unusual or eccentric way of displaying time.” Mr. Walton, 35, currently owns four clocks from Hermès, Cartier and Jaeger-LeCoultre.