Things on this page are fragmentary and immature notes/thoughts of the author. Please read with your own judgement!
Cold vs Hot Water
I've found a cheaper safer way of saving money and water with this problem, put a stopper of some kind on the faucet or showerhead, that way you can block the water from coming out but the water will still circulate in the pipe. A few moments later it's hot.
https://www.youtube.com/watch?v=lE2QFLlEXNw
https://www.youtube.com/watch?v=hwbHs7KUCzE
https://www.rewci.com/whole-house-instant-hot-water-circulator.html
Water Saving Tips
https://www.budgetdumpster.com/blog/how-to-reuse-water/