According to a police officer friend (who was on the county SWAT team), the best location depends on where the sniper is, where the criminal is, and where/how he is holding the hostage.
He said the head triangle (eye-eye-mouth), the middle part of the throat (spinal cord) , or the central upper chest (heart or spinal cord) are all pretty immediate kill shots.
So the sniper will aim for whichever of those gives the clearest shot, with the lowest risk of hitting anyone else.
Snipers, if given the chance, will aim around the nose to top lip, purposely to hit the medulla oblongata, this will immediately severe brain waves to the body. Someone can survive a simple headshot but not this
As I recall this was a minor plot point in “Shawshank Redemption” but regarding different clenching. Is this the case, would a shot or injury in the wrong place (or any place in the brain) case a reflexive action that might include pulling a trigger? I always thought it was a bluff.
In his biography, One Shot, One Kill, the US Marine Corps sniper, Carlos Hathcock drily noted to an observer after Hathcock had shot a Viet Cong, something to the effect of, 'Don’t worry; they flop around a bit after you shoot ‘em in the head. He ain’t going anywhere.’
OTOH, there’s been plenty of police and other video, where head-shot human beings collapse exactly like the “marionette with its strings cut” metaphor used upthread. Like everything else in terminal ballistics, it sounds like ‘it depends.’
I remember once seeing a video from that heist in LA back in the late 90’s where the robbers were wearing body armor. One of them was on a sidewalk trying to escape when a bullet finally found a weak spot and killed him. As mentioned above, it was like watching a marionette fall. What struck me about it was how different that looked from how a living person falls. He was alive while standing and instantly became just a sack of meat. It was very unsettling.