Great post! Just wanted to add that part of the female gaze is depicting female characters as having an interiority, as having thoughts and feelings that are whole and complete unto themselves. For example contrast the women from three different films by Alex Garland.
In Ex Machina the entire plot of the film is whether or not the female robots of the film have an interior existence at all and can it be proved to the male characters. (Granted they are robots but that’s still the essence of the plot).
In Annihilation you have an all female team of women soldiers and each one of them not only has her own motivation for joining the team, but individual relationships with each other. Since the cast is all female there’s no male gaze either in or out of the plot (the audience).
In the third movie, MEN, the cast consists of only two actors, a man and a woman. The lead actress is the motivating force of everything that happens in the movie and all of it is an example of her interiority, as everything that takes place is from her thoughts, about her feelings and memories, and the entire story is told from her point of view.
There really haven’t been enough female directors of movies to really be able to parse the differences in storytelling between men and women in a concrete way, but what I’ve observed so far is that female storytellers often have a different priority of issues they want to show onscreen. Women directors focus much more heavily on the relationships between the characters and characters feelings and motivations even when telling similar stories as told by male storytellers. I talked about this in my post comparing the two different versions of Carrie, the 1976 one by Brian Depalma, and the 2013 version by Kimberly Pierce.
Also there are an increasing number of male storytellers who work in this particular style, like Joss Whedon, Ryan Coogler, and Alex Garland.