This was tested with the (Sense) version, I'm guessing the other three second class cloaks have the same issue but I haven't tested that.
Double clicking this item doesn't cause it to be visually equipped (it stays in your inventory), doesn't give you the stats from equipping it, and it does not appear on your character UNTIL you go through a portal. Once you go through a portal, the cape appears on your character but not in your equip window and your stats still don't reflect having it equipped. Equipping another cape seems to be the only way to remove it visually. Once you can see your character visually wearing the cloak and you try to equip it from your inventory again, you'll receive the error "Fail to install an item."