Comment There is a battery movement that auto sets DST (Score 5, Informative) 291
Clockmaker here, fix things like this for a living.
There is a simple analog battery movement with a secondary clock inside that resets the clock for DST and back again. They work well, are reasonably accurate and inexpensive. Pretty much a "replace single AA battery one a year and ignore it" movement. I have replaced several of the old "Atomic" movements with these.
If you want digital, we call them cell phones these days.