There are actually some products for just that purpose. Examples:

• Aquanta retrofittable water heater controller
• TrickleStar Electric Water Heater Controller

However, modern electric water heaters are well-insulated and I suspect that any savings would be trivial. I'd try this just before going away for the weekend:

1. Select one faucet* and run the water until it is hot.
2. Measure the temperature of the hot water flow.
3. Allow the water heater to reheat the water until it turns off automatically.
4. Turn off the water heater.
5. When you return home, repeat steps 1-2.

I suspect that there will be little change in the water temperature because of the well-insulated tank so buying and the controller will not be cost-effective.

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*A faucet with separate controls for hot and cold water or a faucet where you turned off the cold water supply under the sink would give the best results

When the power is turned off to the water heater it does not stop most of the standby losses as the water in the tank starts at the setpoint, and very slowly goes down. With a well insulated tank, the power to keep it maintained at the setpoint temperature would not be continuous and I would expect to see only minimal difference in standby losses with the power off or on.

Also remember that, if the water heater is in the living space, any energy that is "lost" simply contributes to heating that living space in the winter, reducing the furnace load slightly. However, if you live in an area where it's warm in the summer or you have AC, then the reverse is true at that time of year.

In answer to your original query, you "could save a few dollars" -- but only a very few -- and the breakeven point to offset the expense of installing some complex control system would be years in the future...maybe past the point you are even living there anymore.

Then I'm glad I asked. Little to no ROI is enough for me!