Sounds like a lamport clock or logical clock. Interesting to see it used outside of computer science.

Self emergent clock is still a clock in my books? Just a rather fundamental clock. Clock that makes the time it is measuring? Then again what else is say even an atomic clock. temporal spacing emerging from the changes of state of a physical phenomenon. Solar clock ain't measuring time either. It measures orbital position of Earth and Sun. We then assign these numbers to these changes of patterns. Then we note, oh hey these make up useful repeating patterns.

I'm sure in some goes way over my head way, this is different. However... if the end result (even without directly measuring time) is being able to tell change in time/temporal ordering etc., it is a clock. By certain (at minimum my own definition) of clock. Nice thing about definitions. One can even make ones own.

That's exactly how a clock works - we assign meaning to a state (arm position) and then tie that to time with a battery or winder.