You’re aiming for the medulla oblongata, the part of the brain that controls all the autonomic function like respiration and cardiac function. It’s right at the top of the spinal column. Hit that, and it’s lights out instantly. The easiest way to thin about the location is by putting a stick in your mouth and trying to touch you uvula, and then angled very slightly up from there, basically right through the soft palette.

That’s why a gun in the mouth is so often used in films and TV; it’s essentially correct.