The best time to sell a gun is when you need to or want to sell a gun. Price matters. If you want something to sell quickly, you price it to sell quickly. You don't price it at some sort of "average price" or as I like to say when buying, a "fair price" which is a bit ridiculous as prices are market driven.
I used to particularly enjoy the Jan-March gun shows. You were looking at guns that were acquired before or just after Christmas and availability was good. I have never really thought in terms of when to sell.