With her lilting British accent and a name straight out of Breakfast at Tiffany’s, Holly Golightly is a tailor made introduction paragraph for lazy music writers. But there’s much more to this former Billy Childish protégé than movie allusions and cheap metaphors about the timelessness of her music.

Golightly began her career with Childish’s garage outfit thee Headcoats as a member of thee Headcoatees—’60s girl group meets ...