Normal COI usage is like 3 steps
Double click, go invis, equip COI
Double click with COI on and equipped, become visible
Double click with COI on and visible, unequip COI
That's how it's supposed to work.
How it currently works is:
Double click, go invis, equip COI
Double click while invis, become visible, unequip COI
So you are stuck unable to equip another cloak while the cooldown is going.