If you are talking about a sweep second hand, there are plenty of quartz movements that do that.
If you go for digital quartz, you can get 1/100 second accuracy in a $10 watch.
The longer you time something, the worse the mechanical watch is going to be. Most of them gain or lose several seconds every day.
Zenith is the only manufacturer that I know does significantly better than this, but that particular movement is pretty rare and extraordinarily expensive.
That isn't generally true.
Here's an analog quartz chronograph that has 1/10 second dial: https://youtu.be/mPP3EeWdJsA?t=97
If you are talking about a sweep second hand, there are plenty of quartz movements that do that.
If you go for digital quartz, you can get 1/100 second accuracy in a $10 watch.
The longer you time something, the worse the mechanical watch is going to be. Most of them gain or lose several seconds every day.
Zenith is the only manufacturer that I know does significantly better than this, but that particular movement is pretty rare and extraordinarily expensive.