Step 5: plug the ends of the wand (and fill it)
Carefully dribble glue gun glue into both ends of the wand (one at a time, waiting till each end is set). For the bigger of the two ends, you can pack the end with a little rolled up tissue pushed down a bit with a pencil so that you don't have to use too much glue. For the bigger end you will probably need to have two goes. If you are careful you can achieve a rounded end, as the glue is setting make sure that you rotate the wand to stop it slumping to one side or dripping over the edge. The same goes for the little end, although if you have wound the wand tightly enough, you will not need to fill this twice.
NOTE if you want your wand to be stiff and very robust, then instead of using the tighter rolled up paper core, you can fill it with epoxy resin. Epoxy resin is that sort of glue that you use by mixing up two parts. It can be very runny when mixed up, so you will need to plug the smaller end. After plugging the little end, but before plugging the big end, fill the wand with quick setting, two part epoxy resin. Use the 5 minute setting version rather than the really fast 90 second version and carefully dribble the glue down the inside of the wand, making sure not to get it on the outside. Don't worry If you do get a little bit on the outside though, just wipe it off carefully and quickly, you'll be painting over that later.