After harvesting branches, I let them hang until they are bone dry, way more dry than what you would normally dry for consuming.
I use 5 gal paint strainer bags around the branches, so they catch any falling seeds. I get them in the hardware store in paint supply area.
After shucking the seeds, I wrap them loosely in a thin disposable paper napkin and let them sit in a cool dry place for another 2 to 3 weeks, turning them over each day.
After this, I move them to a small plastic bag with silica desiccant pouch inside, and I put that inside of an air tight storage case, also with silica pouches inside the case.
So the important thing is to dry the seeds out thoroughly and then store them in a way that keeps them very dry, cool, and dark.
Good luck!