This is completely useless, but its a glitch for sure. Mount up your Sandstone Drake, then equip Burgy's hat, then dismount the drake. Youll have Burgys hat on, but it will be a Wizard's hat and you wont have the illusion anymore. Make sure your interface display option is set to show helm. I have also got Burgy to have his hat off (even tho its still equipped) as he stands there with a bald head, but I cant seem to re-do the glitch.