My *old* manual from the 80s states that you should keep two pumps in it (enough to in theory discharge a pellet barely out of the barrel) when storing it. ..............
Crosman.com ...? If it makes you feel better, don't pump it. Whatever works for you, you can re-seal it later, that's much easier than keeping two pumps in it. LOL
I store all my pumpers with two pumps, and first thing I do when taking it out is dry fire it to confirm it held the air.
The 13xx does need to be cocked to be pumped.