One of the earliest and best-known proofs of this came from a Dr. Beaurieux, who conducted an experiment on a French murderer named Languille. After he was guillotined, Languille's eyes and mouth continued to move for five to six seconds, at which point he appeared to pass on. But then when Beaurieux shouted the subject's name, Languille's eyes popped open.
In Beaurieux's own words: "Languille's eyes very definitely fixed themselves on mine, the pupils focusing themselves," and the good doctor continued to get similar results for up to 30 seconds (at which point Languille possibly just got tired of playing decapitation peek-a-boo).