I have a distant relative with a traffic light tattooed in the middle of his forehead, just a black rectangle with red, yellow, and green circles.

And on either side he has some graffiti style writing that I’m pretty sure says “con man”

I became aware of him because we share a fairly uncommon last name, and one day police came to my house grasping at straws looking for this guy because he had been breaking into cars, so the basically went to the first person with the same last name they could find to see if we knew where he was.

It was the first time I’d heard of him, we’re not at all close with the extended family. Eventually I looked him up and found his social media with those stupid tattoos.

I don’t know what actual products are out there, but there are other time signals that could potentially be used, for example GPS.

Off the top of my head I don’t think I’ve seen a gps-synced clock, let alone one with a pendulum, but I’ve also never really looked for one either. It certainly feels like a product that probably exists somewhere to me, I’m sure there’s someone out there who would appreciate a clock that can automatically detect the timezone, whether the region your in observes daylight savings time, etc.

That’s true for mechanical clock movements, but I think OP is looking for a quartz movement that includes a simulated pendulum for aesthetic purposes, which isn’t particularly uncommon, unless your circles include a lot of antique enthusiasts, people who inherited an old grandfather clock, or people who just really dig mechanical clocks (and I won’t knock that, I certainly think they’re neat) odds that a lot of clocks you’ve seen with a pendulum are that type, powered by a AA battery and stuffed into a fancy wooden case

Aside from not needing to adjust the time, is there any particular reason it needs to be WiFi enabled?

Because that kind of feels like an overly complicated solution to a problem that was solved decades ago with “atomic” clock movements.

Which aren’t actually atomic in any way on their own, but contain an antenna to pick up the signal from an NIST atomic clock to set the time (and I believe other countries and regions have their own equivalent if you’re not in the US)

As far as finding a pendulum movement, I don’t really know what is out there, but it may be another avenue for you to look into.