So, there are specific and separate “hunt” and “kill” neurons? Each of those behaviors is complex, not simple. From FT:
The researchers at Yale University used “optogenetic” technology, which switches specific neurons on and off in genetically engineered animals with laser light, to tap into brain mechanisms that control predatory hunting.
By manipulating brain cells in this region through optogenetics, the Yale team found one distinct set of neurons controlled pursuit and another controlled the kill. If the hunting neurons were switched on and the biting set inactivated, the mice pursued prey but could not deliver the killer bite to finish it off.