We have an Atwood like yours, except with no battery
or wiring to the gizmo going into the burner/pilot area. You can buy these water heaters with automatic spark ignition, but I'd guess they are wired into the trailer's 12-volt system.
This looks like it is a battery-powered spark ignition or re-ignition device for the burner. Jury-rigged, maybe, but it may very well work, probably actuated by momentary switch inside the trailer somewhere.
If it works, you won't have to go outside to relight the pilot light
after the storm blows it out.
On the other hand, you'd still have to go out to turn on or off the gas, and I think you'd have no way to know if the pilot light
is out without going outside to peer through the peephole or opening the cover.
What am I missing here?