In the CDC lab, Rick's group is shown a brain scan of a zombie that showed how the infection reanimates a dead person by reactivating the brain stem, which would seem to suggest that only the brain stem is responsible for the walkers being "alive". However, throughout the show, the walkers are killed by basically any blow or stab to the brain in any region, brain stem or not, like this one. How does that work?
According to Greg Nicotero, season 1 head of special effects for the show:
The Walking Dead is "such an homage to the original, George Romero" that there was never a serious consideration to change the cardinal rule that only a headshot can kill them.
As the TWD team from season one onwards deliberately omitted to define underlying facts like the source of the outbreak and the nature of the walking dead brain(stem), I doubt you will find any more canon. Although inspecting the reanimation scene will show an occasional spark shuffling off into other parts of the brain.
So all there is is speculative. And some is based on good forensic knowledge. based on that several parts of the brain can be targeted:
- frontal lobe, "...the zombie frontal lobe is active enough to process sensory input through the thalamus."
- primary motor cortex (exists on both sides of the brain, it sends signals, via neurons, to the muscles of the body)
- brain stem (medulla oblongata)
- upper cervical spinal cord and between the second and third thoracic vertebrae
Putting down your ripening zombie will become easier over time as as the skull itself decays and will be less protected by other tissue as time commences.
In addition of the 'killer' being a survivor and very well trained by then.
In the episode TS-19 they explain that the zombies or "Walkers"
They are not conscious they lack the ability to think or process things like humans do, they basically are not human.
The infection infects the brain stem and only re activates part of the brain.
So logically you would have to decapitate them or shoot them exactly in the infected part of their brain otherwise they wouldn't die right away. I'm not sure exactly how blood affects them, but assuming their hearts still beat internal bleeding could kill the brain, but not immediately.
So to answer your question their isn't enough information to Justify killing a walker immediately with any blow to the head.