this is just one of those "whatta you think?" posts.

would you leave a water heater full of water in a home that is vacant? the pilot remains on so it doesn't cycle at all and the heat is left on during winter.

would leaving the tank full of water cause the tank to corrode even though it isn't being used?

your suggestions/advice and reason for them are appreciated. tia

I'd leave it full...emptying it would just introduce more oxygen and potentially rust. Now, depending on how long it was unused, I'd consider flushing it before reuse or, turn the temp up to max and let it sit for awhile before turning it back down. You might want to turn the supply water off, then, if it developed a leak, at least it would be limited to what was stored in the tank rather than an unlimited supply.

Turn off both the gas and the water to the unit, but leave it full.

The pilot will burn on the order of ~5 therms/month, but the exhaust from that tiny flame condenses on the flue & heat exchanger. In normal operation that condensation isn't an issue since it gets re-heated and blown away multiple times/day on real burns, but for months on end it will (however slightly) corrode the fire-side of the heat exchanger, resulting in slightly lower combustion efficiency. It's pretty minor if it's only a week or two at a time.

Turning off the gas to unused appliances when going away for months at a time increases the odds that the house will still be there when you get back too, eh?