I think he was supposed to keep blinking for a long as he could after his head was cut off. Reports varied.
It's a different story - the one about blinking is told about Lavoisier. AZPaul3 mentioned that one up thread.
I tried to find more details about the Mesmer story; but the fact that Dr Guillotin was part of the royal commission who investigated Mesmer for fraud (together, funnily enough, with Lavoisier) is not helping my googling.