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.