This Relic piece is actually pretty useful when Macro'd in. People knock it for its looks but this equipments DEX+ and Mug is pretty handy. Macro this in when doing Sneak Attack. +5Dex to the head slot is not very common. I also macro this in for mug while in Sky. Without mug, I get between 1,500-2,500 off of Byakko. With Relic head piece, I get between 3,000-4,500 gil off of the same mob.
Other than that, I think SE modeled this piece of relic off of a Shower Cap or something...