This paper is a mess, and it is no accident that contemporary discussions of male gaze tend to elide vast amounts of the material in the paper. It's a mashup of Freudian theory and second-wave radical feminism, and is exactly the kind of garbage you would expect from that combination. Penises are jumping out to scare you on every page, everyone is motivated solely by their penis, their lack of penis, or their fear of losing their penis. The word castration appears on virtually every page -- not an exaggeration.
A short sample:
the function of woman in forming the patriarchal unconscious is two-fold: she first symbolizes the castration threat by her real absence of a penis and second thereby raises her child into the symbolic.
Freud is ludicrous and more or less entirely discredited. Second wave feminism's attitudes towards sex are, while nothing I particularly object to, no longer a particularly dominant set of ideas and for pretty good reasons.
I am not going to go full-on fruit of a poisoned tree here, but the tree from which this particular fruit falls is pretty spectacularly shitty. That said, it's not all wrong. What is going on in this paper is that Mulvey has observed a real thing in cinema (sensible), and wants to explain it in terms of penises (idiotic).
The thing that Mulvey has observed, and which she is interested in, is the male-centric/patriachal aspects of ways these things interact: the movie-watcher looking at the things, people, events in the movie; the people in the movie looking at those same things; the narrative and narrative structure of the film; and finally the way the film is shot, how it looks.
She brings out Hitchcock as as important source of examples, which feels a bit like arguing All men are basically cannibals, let us examine Jeffrey Dahmer... but still, I don't think she's wrong. Hitchcock is just a bit egregious.
What Mulvey sees in movies and their functioning is, once we have cleared away all the penises, this: we watch the movie, and identify (to some degree or another) with the male protagonist. The protagonist admires the girl, and so do we (the cinematographer makes a point of lingering on her legs, her eyes, and so on). At the same time, the protagonist's actions (per the script) drive the narrative forward until the conclusion, when the protagonist gets the girl; by proxy we drive the action, solve the problem, and get the girl.
Ok, so that's a simplistic prototype, and most movies will mess with one or more elements of that structure, but in large strokes it ain't wrong.
Translating this into the land of photographs is obviously going to be a bit of a problem, since there may or may not be a protagonist, a girl, or a narrative. At best, there will be fragments that resemble this bit or that bit. Perhaps we will see a notional protagonist admiring a girl, and admire her by proxy. Perhaps it's just a girl, and we admire her ourselves and/or imagine a protagonist to admire her also. And so on.
Mulvey notes explicitly that this material only works for film, so we know we have some spadework to do if we're to make a go of it in still photographs.
I don't see a clean way forwards into still photos unless we simply drop the protagonist out entirely, along with our identification with the protagonist and that whole proxy relationship. In the general case, it's just us, looking at the picture, at the things in the picture. Maybe we identify with the photographer? I don't see it as a generally useful model, so I am going to stick with a model of just us, looking at the picture. No protagonist, no narrative. We get to keep the part about how it looks, the cinematography, intact, though.
So what is a "gaze" in some sort of general sense?
In the modern usages that I have observed, "gaze" is associated with authorship, but Mulvey has no part of that. For her, there are conventions in mainstream cinema, all slanted toward a male viewer's comfort and pleasure, and anyone making a mainstream movie whether male, female, or amphibian, would obey those conventions and produce more or less the same sort of thing.
There are real problems with the idea that authorship in some way unconsciously shines through in a photograph, namely, it doesn't.
Therefore let us explicitly separate authorship off.
To get further it seems to me that we should step back slightly, and think about how a movie, or a photograph, works.
As the post-modernists would happily tell you, everything in these forms of media is "coded" for our viewing pleasure. We recognize a bride and a groom, deduce the social ritual of a wedding, and then by the expression on her face we learn (we think) how the wedding is going. I confess that I would likely not recognize a Chinese bride, or an Armenian one, and the photograph, or film footage, would lose much of its meaning for me. Which is how we know these things are coded -- when you don't have the keys, you can't understand it.
You might say, perhaps, that landscapes are not coded? Well, suppose you were a Martian, a desert landscape and a rain forest landscape would be either incomprehensible to you, or have quite different meanings, so there. Landscapes are also coded, just in rather more broadly understood codes.
With this simplification I think we can reasonably take a "gaze" as a subset of the codes in play, those codes associated with the pleasures, the preferences, the comforts of some specific category of viewers.
Now we are getting somewhere!
Male gaze in a still photograph is whatever elements are coded in the thing which give pleasure or comfort to a male viewer. This could be a beautiful woman posed in an available way, or if we allow the radical notion that a man is more than a walking penis, perhaps something to do with cars, power, money, strength, dominance, or any of the other stereotypes. Does a picture of my five year old daughter smiling constitute an example of dad gaze or is it just more male gaze because my pleasure is basically just pride in my virile ability to produce and support heirs?
Female gaze then becomes whatever would make women happy, fill in, I suppose, the stereotypes of your choice. Black gaze becomes rather dicey if you're just jamming stereotypes into the frame.
Setting aside the whole (tongue in cheek) issue of stereotypes, we might discover that multiple gazes could in theory be present in a photograph. Suppose a photograph produced pleasure and comfort for both men and women who happened across it? By casting the idea of "gaze" in terms of comfort and pleasure, we deny the idea that "female gaze" is somehow the opposite of "male gaze" (which, as I have observed in the past, is not a concept that readily admits an opposite.)
In this formulation, one "gaze" does not rule out another. No "gaze" is unconditionally the opposite of another. Conflict may occur, where one category of viewer finds pleasure and comfort in something another category finds unpleasant, or discomforting, but there's nothing in the idea of "gaze" itself, here, which insists on conflict.
We find also, under this understanding of "gaze" that much of what gets promoted as "female gaze" is anything but. It is not at all clear that photographs of the female artist, naked but unavailable, and visibly peeved, produce all that much pleasure and comfort to the female viewer. I am not convinced that anyone at all would find any kind of comfort or pleasure in Talia Chetrit's Showcaller. In my formulation here, Showcaller lacks "gaze" entirely. This is not a criticism of the book, note, but merely a consequence of this definition of "gaze."
We can see, now, that opposing "male gaze" (which Showcaller arguably does) does not produce a "female gaze." You can probably make the case that Showcaller (and innumerable similar pieces) are a critique or an attack on "male gaze."
Like Humpty Dumpty, you are free to use words as you choose, of course. If you choose to mean by "female gaze" nothing more than an attack on "male gaze" well, so be it. That does seem to be the common usage.
It is not, however, a particularly useful usage, nor is it particularly aligned with the meaning of "male gaze." I like mine better.