I have a few things to add
As I understand it, agencies like the Mossad have assassinated people by using a .22 to the brain. The idea is the bullet bounces around the brain cavity and tears it up.
On the other hand I shoot a .40 cal with personal defense rounds, they split and mushroom on impact with a little pike to grab the meat and carry it on its path out of the skull. Massive hydrostatic shock and tissue loss. A solid hit is probably a fatal one.
I came out of the ER after a car accident and saw a guy who had been shot at point blank range with a .375 magnum and the bullet skipped off of his skull. It split his scalp open and he was telling the story holding a big wad of gauze on his head.
The point being that there are a wide set of variables, but I think that if you damage the Medulla Oblongata you are toast, Doc’s?