“They all think it’s hilarious,” Mr. Getz said. “But they know that only I would wear this cheap, knockoff watch with my own face on it as a cartoon — and pretend to be proud of it.”

Fun watches, after all, are rooted in self-expression. The Washington, D.C.-based watch collector Abduljabar Totonji bought his Joker sight unseen after first coming across it on social media, and the piece became his collection’s third watch (preceded by a Rolex GMT-Master II and Omega Speedmaster).

“The Joker spoke to me and I just felt like I had to have one in my collection,” said Mr. Totonji, who added that he sees himself as a fun person who enjoys meeting people (he regularly hosts watch collector meet-ups in the Washington area). “I try not to take myself too seriously and try to enjoy myself with the collecting as well.”

Mr. Totonji likes unusual watches that tell time in an esoteric way — like his Raketa Russian Code, that runs counterclockwise — but he also has been drawn to independent watchmakers because they resonate with him professionally (he is the chief investment officer at a real estate investment business that has just 15 employees). “I take my work seriously — and I know they take their work seriously,” Mr. Totonji said.

Humor is infectious, and so, too, is sharing the joke of an irreverent watch with others.

Marko Koncina, the Zurich-based founder of the watch media platform Swiss Watch Gang, owns a Joker as well as the new Sequent Smart(ass). The smartwatch (priced at 545 pounds in Britain, $549 in the U.S. and limited to 160 pieces) was codesigned with the French artist and watch collaborator Romaric André, known as seconde/seconde/, and was intended as a cheeky motivational piece, featuring a step counter whose indicators say, “Shut Up, Push Harder,” and other off-color exhortations.

When it comes to the Joker, people “either think it’s super expensive or a child’s toy,” Mr. Koncina said. “For me, I don’t care. But when there’s that one person who knows what it is, we connect immediately. We’re like brothers.”

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