In 2012, he started to design the Legacy Machine Perpetual, a 581-component watch with his revised perpetual calendar option — which wasn’t working. “I am driven mad by watchmaking,” Mr. McDonnell said, “and this was excruciating, I was in bits.”

By 2014, Mr. McDonnell had moved back to Belfast and was beginning to assemble a prototype of the design. “It was a disaster,” he said. “Absolutely catastrophic. The day-changing mechanism didn’t work.” But then, one Monday morning, he was back at his bench, “and the solution fell right out of the sky! It was so simple and elegant — just one little lever was needed, an extension to an existing lever.”

The Legacy Machine Perpetual was introduced in 2015 in two versions, red gold for 138,000 Swiss francs ($147,590) or platinum for 168,000 Swiss francs. And the following year it won the Grand Prix d’Horlogerie de Genève in the calendar watch category.

“This was Stephen’s revolution in the history of watchmaking,” Mr. Büsser said. The watch, one of MB&F’s best sellers, has sold more 250 pieces and “not one has come back with a perpetual calendar problem,” he added.

Last year MB&F introduced the Legacy Machine Perpetual EVO, a sportier version of the original; there is a three-year waiting list, Mr. Büsser said.

Mr. McDonnell, who has worked occasionally for other brands but is not authorized to name them, now is collaborating with MB&F on “something new and very complicated,” he said, which is to be released later this year. “They give me total carte blanche,” he said. “It’s wonderful, but it’s also terrifying. I don’t know how many more watches I’ve left in me.”