Hi,
Good heater has already good insulatiuon. As far as I know I never saw
heater firing up when hot water is not used. Our heater is located in
the insulated basement utility room with gas furnace, water softener.
Tony

then a timer will save nothing. but run up your electric bill a tiny
amount for the timer

I had a hopt water tank fail as I was leaving for a 2 day trip. Leak
was at the top. I turned off the water and left.

2 days later I returned and the water was still hot enough for a
shower. I turned the water back on and let it leak.

tank insulation has really got good.