Algol is a useful test of how much of a star's traditional character is actually attributable, because the gap between the source and the modern delineation is unusually wide.
Ptolemy gives two planets, Saturn and Jupiter. That is the whole of it. There is no mention of decapitation, of hanging, of violent death, of strangulation, or of any of the specific horrors that fill modern entries.
Those specifics accumulate through the medieval Arabic and Latin tradition, where the star is Caput Algol and is used in talismanic magic, and they reach their familiar English form in Robson in 1923. Robson's entry for Algol is the most alarming in his book and is quoted constantly. He was compiling: some of it is from Ptolemy, some from the Arabic material, some from Renaissance sources, and some from nineteenth-century writers whose own sources he does not give.
Agrippa includes Algol as the first of the Behenian fifteen, pairing it with diamond and with black hellebore, a genuinely poisonous plant, which is consistent with the star's character and is a good illustration of the internal logic of the Behenian scheme.
The Gorgon association is worth one observation. Perseus holds Medusa's severed head, and Algol marks the head. Whether the constellation figure was drawn to place a variable, ill-omened star at the point of severance, or whether the star acquired its character from an already-existing figure, is not determinable. The Greek constellation figure is itself inherited and reworked from Mesopotamian material, and the chain is not traceable that far back.