I think you have fascinate all wrong. The root is fasc whose core meaning is to bind. Fascist comes from the Roman symbol of thin twigs of bound together. Individually, each twig is easily snapped, bound tightly they are virtually unbreakable. It is an undeniably strong metaphor even if it was adopted by a rotten ideology. The phallic amulet’s name is probably an obscure back-derivation.

One fascinates by fastening someone’s attention.