Horologist

The Fourth Doctor, when asked if he was a clock expert, claimed to be both a horologist and a chronometrist. (TV: The Sontaran Experiment)

Bilis Manger was a horologist.

Behind the scenes
In real life, a horologist is an artisan who makes and repairs watches. Since a majority of watches are now factory-made, most modern watchmakers only repair watches. However, originally they were master craftsmen who built watches, including all their parts, by hand.