Look down his throat just in case he has any thin strip of plastic caught on the side of his throat. Im curious why he would have the reflex to want to gag? wouldn't hurt to check him out! for your own sanity. My tilly was always finding staples or anything metal and one day she kept having this gagging reflex so I opened her mouth anyway and sure enough there was a staple
stuck on the back of her throat, Wasn't to fun for her or me..
keep us posted..