I have a button cover for it but haven't put it on. There's a piece of wire with it, do you know what it's for?
That piece of wire should be a thread. It is to make the button cover fit snugly. If you lock the fire button by turning it clockwise, lay the thread over the top of the button, then press on your button cover, it should be a nice snug fit. Make sure the fire button is locked (will not push down) when fitting the cover otherwise the switch mechanism might get bent or broken.
Yours is a beautiful Reo Mini 2.1 SL, a wonderful mod, they are my favorite, along with the 18490 Woodvils. Welcome to Reoville.