Some of these re-circulation pumps have 2 settings, automatic and timed.. automatic for thermostat control, and timer for timed operation.
The electric cost varies .... $14-18 for 1 year continuous operation.
The pump does not harm anything if left ON ... except shorten lifespan of product so you would also calculate replacement cost...
... However you can buy a thermostat that clips onto the pipe to turn the electric power on and off.
Specs and manual shown following link:
http://waterheatertimer.org/Water-heater-recirculation-system.html#clip If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7
I was having the same problem and came accross these instructions. The following link is a PDF file. The first page relates to an analog timer and the following pages relate to a more advanced digital one. Good luck.