How to get power only when ignition is on?

I'm assuming your "battery gauges" that you wish to install are voltmeters, not ammeters. The broken gauge on your dashboard may be an ammeter (i.e. it shows whether the battery is currently being charged or discharged, not the voltage present in the electrical system). If they're ammeters, you may not need separate power supplies to the meters, but you do need a shut or some other current sensing device to measure the current.

The instrument panel has an ammeter, but it is broken, showing "charge" at all times.

I am installing voltmeters. These, in particular:

http://www.amazon.com/gp/product/B00CULEO9A

If they're voltmeters, and you have a somewhat typical sort of battery isolator that connects the two electrical systems together when the engine is running to charge the house battery, you won't really get much useful information from the separate meters. They'll show the same voltage as each other, minus whatever line losses occur between the batteries. You would be able to see if the isolator relay was not connecting properly, but that's about it.

My 1990 Winnebago Warrior has a three-way switch. If you switch it to the left, it will stick there and will gang the engine's alternator to the house batteries, charging them. So in this state, yes, both battery gauges should read the same voltage while the engine is running. However, I don't think in this position it allows charge to go from the house batteries to the engine battery. So when the engine is off, even in this position each gauge should represent the voltage state of the house and engine batteries separately.

When the switch is to the right, it is momentary only. You can hold that down while starting the engine, and in this position it gangs the house battery to the engine battery to allow you to start the engine from the house batteries if the engine battery is dead. This is momentary, however. But in this position, again, both gauges should read identically.

When the switch is in the center, the house and engine batteries are isolated from one another. In this position, both gauges should read independently.

A simple pushbutton for each meter to turn it on momentarily might be more useful in general, truth be told. You could then check on them at any time, parked or not, and ignore them otherwise (and not have possibly bright readouts blazing on your dashboard when you're driving at night).

I thought of this, but I don't want to have to keep checking while driving if the alternator fails and I'm running on battery unknowingly. I want the engine battery indicator at least on when the engine is on. Might as well have them both on when the engine is on as it will show me the state of my house batteries and, if charging, I should see a "full gauge" for sure.

Steve