It sounds like you are describing two different problems.

FIRST PROBLEM: Turning off a hot water heater.

First, there are two ways to hook up two water heaters: series and parallel.

SERIES

• In series, the water comes in to the first water heater, then passes through the second hot water heater, and finally goes to your fixtures.
• If you turn off the second water heater, then the water in the second one cools down between uses. This results in very long warmup times.
• If you want to turn one of these off, turn off the first one. (This is actually a legit way to save on energy costs if you don't need the extra hot water volume because in many places the water supply is colder than room temperature and the first tank allows the water to sit and reach room temperature before it's heated.)

PARALLEL

• In parallel, the incoming cold water is split between the two water heaters. Hot water coming out of the two heaters is combined and sent on to the fixtures.
• If you want to turn off one of the water heaters, you also have to close the valve to the inlet or the outlet. Otherwise you will just be mixing the cold water in one water heater with the hot water from the other heater.
• Leaving one heater closed off for a long time is a bad idea because the water can become stagnant and foul.

SECOND PROBLEM: Pilot light going out

Just turning off one heater should not cause the pilot light on the other to go out.

I have also considered doing this, but have not so far (inertia). One way to do this is to add a separate single faucet for the electric water heater and T off the cold supply. That way when you use the hot you don't leave hot water abandoned in the piping. If you T off the hot supply, you will leave hot water in the lines when you are finished with the hot, but you will have a full flow of hotter water.

A small tank can allow you to have on tap at gallon or two of very hot water even using the 120 V circuit which is probably there to power a disposer. If like a lot of people you have removed the disposer, you could use the receptacle for this. If your disposer receptacle is on a dedicated 20-A circuit, this would work very well, but if not, you could use the disposer wall switch to turn off the heater when high power appliances are being used with other receptacles on this circuit.

A tankless heater would have to be at least 30 A at 240 V to give a decent flow of very hot water. You would have to have add the cost and trouble of adding this circuit to the project, but this would be ideal.

EDIT

One of these very small tanks with its own spigot (presumably rated for very hot water) might be the best choice. You don't want to run very hot water (200 F) through a standard faucet.