I'm certain I've seen clocks which pause on the minute like the stop-to-go ones sold in rail enthusiast magazines, railway museum gift shops etc. many years ago. Obviously, they don't include an actual stop-to-go master/slave system, they just fake it.
They used to make stoptogo versions back in 2001 but discontinued them because it loose or gain 20s a day.
The real ones get a pulse over the power line from a master clock every minute setting the time. The rotation of the seconds is just a motor using the electric grid's 50 Hz.
I meant a physical wall clock, not an app. I suppose I could mount and iPad on my wall and run the app, but I don't want to spend several hundred dollars on a clock that will sue me.
You can get master clocks and slave clocks on eBay, antique or not, with lots of character or not. But they're a pain, since you need to connect the slave to the master with a cable.
Actually - you can get a little circuit board to drive the slave clock without needing a master clock. It mounts to the back of the clock. See here (in German):
