From Guillot, the French diminutive for William. The family may have come with William the Conqueror into England, from Gillette, a town in Piedmont, France. Gillette, the son of Giles.

Arthur, William (1857) An Etymological Dictionary of Family and Christian Names. New York: Sheldon, Blakeman. Public Domain.

GILLETT. See Gillet. GILLETT. "In England there are numerous families who write their name Gillett and Gillot, all of French extraction ; the former at Glastonbury, Exeter, aud Banbury ; the latter at Birmingham aud Sheffield. It is probable tliat these names, as well as Jellett and Guillot, have all been originally the same, namely Gillot, the diminutive of Gilles, the French form of Giles." Ulster Journal of Archseology — SBcl duVifo.

Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.