The light goes back OUT once it lights.
If the light stays on the appliance isn't getting propane. When I change my tanks I generally turn on the stove to purge air out of the lines, then light the water heater.
There may be a turn off valve at the water heater too. If it's been turned off, then it's simple to turn back on. BTW this is something that you don't have to go to an Airstream dealer to get fixed, any competent RV tech can troubleshoot it.
I do hope you got a complete stack of manuals with your unit, if not the manufacturer may have one online.
Today is a gift, that's why they call it the present.