@ZeissIkon The novel is vague on the requirements to become a vampire, so subsequent fiction has offered multiple interpretations. The "three bites" method was probably directly inspired by Dracula's multiple visits in the novel, but the novel was almost certainly inspired by older folklore where it is common for victims to be visited multiple times before death results (vampire attacks being used to explain wasting diseases before the advent of germ theory).

To add to this answer, the novelization states "The light of the Great Conjunction would irradiate the Skeksis with energy, but a left-handed energy only, darkly colored, rich in malevolence." In other words, the Skeksis seemingly derive their immortality from the Darkening itself. This seems to make them both dependent on it and mutates their bodies in the process.