The link came about partly due to both women being close in age, also because they were related and due to Eileen being very much her own character and not a fairy royal puppet, the way the Queen would like her to be. (Eileen would stop asking awkward questions about royal magical conduct if she were such a puppet for one thing). Eileen had also, in the course of writing her own books, researched the Witch's past properly. Empathy can be a powerful thing. And it led directly to the Witch sparing Eileen's life at least once, something nobody else was privileged to receive.
The other link I like a lot is the one between Melanbury, aristocrat in her own right and L'Evallier's wife, and Hanastrew, who is far more "common", proud of her mentor, Eileen, and would only speak with a plum in her mouth if she was actually eating the fruit in question at the time! Both Melanbury and Hanastrew (a) want to have careers (more of an issue for Melanbury as with her noble background this is very much frowned on) and (b) want to prove to be more than decorative and (c) serve the Kingdom well. Hanastrew is the only person Melanbury would confide in and even that posh lady seems to need her own girlish confidant. Hanastrew does not envy Melanbury's posh background, can see its disadvantages clearly and other than hating Melanbury's passion for salads (Hanastrew loves her chocolate and puddings but is active enough to burn off everything she consumes) likes the girl elf a lot. There is more to both girls than meets the eye and both sense that in the other.