I believe the term you’re looking for is foudroyante

That mechanism has a small hand make one revolution each second, divided by the frequency of the balance.

Foudroyante watches are pretty rare and uncommon.

Something similar is the Zenith Defy which has a small seconds hand make one revolution every 10 seconds.

CWC G10. Not quite dirty dozen but it is a legit military issued quartz field watch following that lineage with a very similar design spec.

Edit: clarity

Similar to me, had the XV, sold and regretted so found another XV. Now it’s never leaving my ownership again haha

I see every mark ont he watch as me making the watch mine. Nobody else’s watch has gone through what I have with it. It’s mine and mine only. When I build memories while wearing g the watch or have an experience with it on like a holiday or whatnot, it takes on a deeper role as part of what makes me “me”. I’m not perfect, I’ve hurt myself, I’ve done some fun stuff and some pretty damn amazing stuff. I now see watches on my wrist for those moments just a part of the whole experience. It no longer matters if it gets marked or scratched. That’s all just part of the ownership and like a rite of passage to make it mine.