The ordering of events around Algol is the single most instructive thing about it, and it is regularly told backwards.
Algol's malefic reputation is ancient. It is the Gorgon's head, associated with decapitation, and it is the most consistently ill-omened star in the astrological tradition. Ptolemy gives it the nature of Saturn and Jupiter; the Saturn half carries the entire grim reputation, and the Jupiter half is so routinely forgotten that most modern accounts describe Algol as simply Saturnine.
The variability was documented far later. Geminiano Montanari noted that the star's brightness changed in 1667, without establishing periodicity. John Goodricke, a deaf English amateur astronomer then aged eighteen, determined the period and presented it to the Royal Society in 1783, in a paper titled A series of observations on, and a discovery of, the period of the variation of the light of the bright star in the head of Medusa, called Algol, published in the Philosophical Transactions. He proposed that a dark body passing in front of the star could account for it, which is correct, and which anticipated the concept of an eclipsing binary by a century. He was awarded the Copley Medal and died at twenty-one.
So the reputation predates the discovery of the variability by at least fifteen centuries. Algol was not called the Demon Star because it winks; it was called the Demon Star, and much later someone noticed that it winks.
The frequent modern claim that ancient observers knew of the variation and named the star for it is therefore not established by the naming. There is a specific proposal that an Egyptian calendar of lucky and unlucky days from around the thirteenth century BC encodes Algol's period, based on statistical analysis of its day ratings. That claim is interesting, it is published, and it has been questioned; it should be reported as contested and not as fact.
Sources AstronomyAndrew Fraknoi, David Morrison, and Sidney C. Wolff (OpenStax) with TetrabiblosClaudius Ptolemy