On a new well insulated tank, how much do you think you're gonna save with a timer? You won't save anything until the water cools down below the point that it would have come on. And my bet is by that time, the timer will be about ready to turn it back on anyway. The bottom line is that especially with an electric tank, which is completely insulated, the water cools so slowly when it's not being used that it isn't going to make a difference big enough to make the installation of a timer worthwhile. And if you have to pay an electrician to do the install, I'd bet you come out a big loser.
As an experiment, you could measure the temp of water coming out of a tap close the heater at night. Then shut it off and measure again in the morning. I'm going to try it on my gas water heater.