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Always wipe down every gun with an oily cloth, regardless of how it is kept.
My preferred lube and protectant is Corrosion-X but there are plenty others out there that work great.
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This works - and don't touch the metal surfaces after wiping them.
I've had 03's, 03A3's, M1917, etc. in those padded cloth zip up cases, stored in the attic (freezing in the winter, 110F and humid in the summer) for 6 to 8 years and when I took them down they were as nice and rust free as when I wiped them off and put them away. Plain old 3n1 oil.
I had some guns stored in the attic (same storage method) at my mom and dad's house for over 20 years (father-in-laws hunting guns) and took them down once in all those years to inspect and wipe them down again. They all looked great, no rust, nice and shiny. Finally took them down to give them to my sons and nephew (his grandsons) when they got old enough to take care of them and have a place to store them.
In my experience, if you get rust you either touched it (finger tip/palm) or failed to wipe it down well.