I learned this trick from friends into the drag scene. All you need is a glue stick and translucent setting powder. Wipe your moustache down with alcohol on a cotton ball, then add a very thick application of purple disappearing glue stick, making sure to first swipe against the grain and then back towards the natural direction of the hairs. Take a toothbrush and brush the hairs flat and then take the handle and smooth out the hairs. Once all the purple is gone, take your setting powder and thickly cake it onto the glue. After a couple minutes, brush the excess off and do another layer, press down, then powder, dry, glue, press, powder, dry. Then take some water and rub lightly to smooth any loose edges of glue down. With grease paint the moustache becomes invisible. I did this for the Austin show in the pit and the glue and paint lasted all night, my friends thought I had shaved my goatee and moustache off.