In some seventy years of shooting rifles, I've yet to see any shot into the brain with a high-intensity cartridge which did not result in instant flop. (Several javelina and whitetail deer, and a few feral dogs.) I'm reasonably convinced that the same holds for shotguns and major cartridge handguns. Since the brain has no nerves to signal pain, any quivering does not represent what we normally think of as "suffering".
I have seen animals bounce about after a brain shot from a .22 rimfire, but, again, no pain in the brain. Just disconnected motor signals to the extremities.
You're from BATFE? Come right in! I use all your fine products!