I'm not sure if this is an intended feature with an internal cooldown to prevent spamming, but I figured out how to correctly break incognito. I have the ability on a keybind to quickly toggle my disguiser on and off. If you do it too fast the system cannot keep up regardless if you're spamming it or simply toggling it in a quick succession. You'll know it's completely broken when at the bottom right of your screen the prompts for "Equipped X Skin or Holstered X Skin" won't appear.
What also will happen is once you completely break the system by either spamming your Toggle or using your Toggle too fast for it to register or load the sequence of taking off your skin. The current round your skin will still appear with your name being disguised, however the following round your skin will be holstered.
