Another idea on this (I've been doing this for years, but I really don't know what these CLEAN gloves you're talking about).
I have a small bucket that used to hold dishwasher pellet thingies in. It's about 12" tall by 10" wide by 6" deep & has a flip-top lid. I punctured a small hole in the side & hung it from a nail from my garage wall. Then I put all the gloves in there. That way, I don't have to wander around trying to figure out where did I put my gloves the last time I used them. But I've been folding them in like socks for.. well, as long as I've been gardening (2 years)