16 g is what I use too. It's available at Lowe's, tractor supply, etc. It holds its shape very well. I've also used it successfully for a buttplate. Probably a little overkill for a patchbox, but easier to work with, also, in some repects, as it resists kinking and creasing better than thin stuff.
The 22g is better for one-piece nosecaps, plain ramrod pipes, small inlays, etc. Sometimes it is easier to make a fine patchbox hinge out of 22g and rivet/solder to 16g door and finial. I think 7 knuckles is my best effort with 22g and 5 with 16...But I've made practice hinges with 9 knuckles, it just gets to the point where even my small files etc. are too awkward and I can't even meet my low expectations!