Dear LC,
I think that most of the cell reactions can be characterized as chemical clocks. As long as there is homeostasis, that is, that is, control parameters, there will be a clock of some kind, not even if is not regular in time. Like a thermostat. Not, that this is not the same of a random reaction, since in this case the chemical reaction will simply follow the 2nd law of thermodynamics and defuse energy, where a chemical clock is a physical analogue to engine. On the other hand,a clock is more akin to a Carnot cycle.
The idea of a chemical clock came to me when I was considering the case of pH regulation of a cell, the ion transport. This is the most trivial active function of a membrane cell, in my view, other than the most trivial function, that is no to let the contents of the cell to spread to the environment. The ion transport is like a little machine, that is always pumping ions in order to keep the pH around a certain level.
The idea is to consider the most primitive example of life, a kind of self controlling cycle. Some thing I had to exclude, to try to get in the most basal level I could thing of. I can get rid of a membrane if the elements needed for are abundantly available in the primitive ocean.
I can get rid of reproduction if there is no defined requirement for perfect conservation of information. The sequence of stages required for the working of a clock is itself information. I don't know what is the original sequence, but I tried to propose one that would work like one in the primitive ocean. Also, as I posted in the additional information (BK reaction can be thought of composed of sub reactions) and also gave a certain mathematical treatment in section 2, different cycles could superimpose into a different one. Also, due differences in composition due the depth of water and environment, there should be some sort of competition for which reaction could thrive.
In the large ocean, cycle waves would compete, like these ones, in a petri dish. Just imagine that the ocean is a thin layer over a huge surface.
https://www.youtube.com/watch?v=zDgx6n6aExE
I also proposed that, after a long time, these reactions would be strong enough, or adapt to, the kind of environment rich in organic material, like, in alkaline vents. The presence of stuff like lipids and rna, would select much more complex reactions on the long term, like those which happen in cells.