Is a coracle made from animal skins stretched over wooden frames equivalent to Cousteau Society's turbosail ship Alcyone? Could anyone sail at 65 knots without advancements in tech (sailrocket.com)?
Could I fit an entire library of books in one pocket without the technology in my Kobo?
I'm not familiar enough with horse riding to provide a better example, but the high-backed cavalry saddle and stirrup were, at the time, considered advancements in military technology. Even the fact that you can ride horses for pleasure rather than by necessity is thanks to technologies such as the automobile.
People continue to do these things, but they have not always done them in the same way. And when the newer way is better, the old way rarely survives, except as a historical curiosity. Mechanical timepieces are objectively inferior to both electromechanical timepieces and purely electronic timekeeping. There's a reason why no one has to go up twice a year to wind the mainspring on the GPS satellites.
If you don't have electricity, and you are not navigating an antique wind-powered ship, you probably don't need a mechanical timepiece.
Also, I recall, from way back in the 1980s, a digital clock that was "powered by a potato", using zinc and copper probes. Even if we lost all grid power, and solar cells, and low-head hydro, we could still manage a zinc-copper cell battery.
Didn't you see that episode of Breaking Bad?
The 555 was first sold in 1971. Why the hell would you still rely on complex mechanical linkages to track the time when you could just start believing that digital watches really are a pretty neat idea instead?