Taper isn't THAT foolproof because it won't work as reliably against higher-level charm spells or against NPCs thst have buffs.
Assign a hotkey to "switch between last two targets" in your hotkey options and use that to invis yourself and still be able to switch back to your pet immediately to root/mez/nuke it.
Watch my videos if you care to. You'll see me hitting f1 to swap targets between myself and pet at the end of a pets lifespan so I am use my ~ key to swap between the two of us to break charm and reacquire target on pet quickly.
As for invising your pet? Lol. If you don't notice you are about to invis your pet instead to yourself, then using taper you'd also be as likely to dispel yourself as your pet.
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