The first use of the term “male” gaze, in 1975, was in an essay by Laura Mulvey:
In a world ordered by sexual imbalance, pleasure in looking has been split between active/male and passive/female. The determining male gaze projects its phantasy on to the female form which is styled accordingly. In their traditional exhibitionist role women are simultaneously looked at and displayed, with their appearance coded for strong visual and erotic impact so that they can be said to connote to-be-looked-at-ness. Woman displayed as sexual object is the leit-motif of erotic spectacle: from pin-ups to striptease, from Ziegfeld to Busby Berkeley, she holds the look, plays to and signifies male desire. Mainstream film neatly combined spectacie and narrative. (Note, however, how the musical song-and-dance numbers break the flow of the diegesis.) The presence of woman is an indispensable element of spectacle in normal narrative film, yet her visual presence tends to work against the development of a story line, to freeze the flow of action in moments of erotic contemplation. This alien presence then has to be integrated into cohesion with the narrative. As Budd Boetticher has put it:
“What counts is what the heroine provokes, or rather what she represents. She is the one, or rather the love or fear she inspires in the hero, or else the concern he feels for her, who makes him act the way he does. In herself the woman has not the slightest importance.”
…Traditionally, the woman displayed has functioned on two levels: as erotic object for the characters within the screen story, and as erotic object for the spectator within the auditorium, with a shifting tension between the looks on either side of the screen. For instance, the device of the showgirl allows the two looks to be unified technically without any apparent break in the diegesis. A woman performs within the narrative, the gaze of the spectator and that of the male characters in the film are neatly combined without breaking narrative verisimilitude. For a moment the sexual impact of the performing woman takes the film into a no-man’s-land outside its own time and space. Thus Marilyn Monroe’s first appearance in The River of No Return and Lauren Bacall’s songs in To Have or Have Not. Similarly, conventional close-ups of legs (Dietrich, for instance) or a face (Garbo) integrate into the narrative a different mode of eroticism.
The male gaze is a term of art a feminist critic gave to aesthetic conventions she observed in many films, not a statement of biological determinism, or a statement about men in general. There’s no reason to think that “the male gaze” can only be produced by men, and it’s not hard to think of counter-examples of female filmmakers utilizing the male gaze (i.e., the Pheobe Cates bikini scene in “Fast Times At Ridgemont High,” directed by Amy Heckerling).
I’m not sure it’s coherent to speak of “the male gaze” outside the context of discussing a piece of media. A person doesn’t have “the male gaze”; only a piece of art does. (As I understand it.)