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Torah scroll.
Sefer Bamidbar opens with G-d speaking to Moshe “in the wilderness of Sinai, in the Tent of Appointment”.  Why “in the Tent of Appointment”?  Bamidbar Rabbah answers that while G-d had previously spoken to Mosheh outdoors and in front of the entire nation, “once the Tent of Appointment was stood up, He said: “Tzeniut is beautiful.  But wasn’t tzeniut beautiful all along? Does G-d k’b’yakhol regret the public Revelation at Sinai?
Bamidbar Rabbah continues by citing Tehillim 41:11: “The glory of a king’s daughter is within; her clothing is set with gold”.  This demonstrates that Chazal saw Divine tzeniut as a model for women.  Does tzeniut for women becomes a primary value only once they enter their appointed tents, whereas until then the goal is to attract their bashert, as G-d needed to attract Moshe at the Smoldering Shrub?  Was Sinai a chuppah?
Shemot Rabbah 41:5 takes the connection one step further. “He gave to Mosheh kekallato speaking with him at Mount Sinai” (Shemot 31:18) – Said Resh Lakish: Just as a kallah (bride) is matznia herself while in her father’s house, and no one can recognize her, but when she comes to enter the bridal canopy she reveals her face, as if to say “Let anyone who knows testimony against me (that I have not been tzanua) come forth”, so too a Torah scholar must be tzanua as this bride, and yet publicly known for his good deeds, like this bride who publicizes herself.  On this basis they said: A woman who is matznia herself, even if she does not descend from kohanim, she is worthy to marry a Kohen and to raise High Priests. Here Divine Tzeniut is modelled after women’s tzeniut, and then serves as a model for scholarly tzeniut.
This desexualizes the concept of tzeniut.  There is no fear of eroticism behind Resh Lakish’s requirement for scholars to avoid publicizing their good deeds, and no need to eroticize G-d’s preference for privacy when talking to Mosheh.  The midrash assumes a conceptualization of tzeniut that encompasses all three contexts: physical intimacy, deeds, and Divine.
The analogy remains inexact, however, because Mosheh actually never sees G-d’s face. That gap is important. Without the gap, we might read Resh Lakish as setting up objective requirements of facial tzeniut.  With the gap acknowledged, we must read him instead as establishing a standard relative to the general and specific social circumstances of the bride. Even though Moshe never sees G-d’s face, human brides and grooms must see each other’s faces before marriage.
Shemot Rabbah concludes that a woman who is tzanua merits raising High Priests.  This connection is derived from Tehillim 41:11’s reference to clothes with golden settings, alluding to the High Priest’s official wardrobe.
The connection is concretized by the case of Kimchit, found in  Vayikra Rabbah (Acharei Mot 20). Kimchit had seven sons, all of whom served as High Priest. The Sages said to her: “What have you done to merit this?” She replied: “In all my days the walls of my house never saw the braids of my hair.” They said to her: “Kimchit, all the kemach (flour) you have made is finely sifted”.  They applied to her the verse “The glory of a king’s daughter is within; her clothing is set with gold”
This seems to be a valorization of extreme physical tzeniut.  Kimchit kept her hair covered at all times, even in her own house, even when it was braided, and even when there was no one to see it but the walls.
On Yoma 47a, however, the Rabbis respond skeptically to Kimchit: “Many have done what you did, without achieving the same result”, The phrase “many have done … but … ” appears on Niddah 69b-71a, where the people of Alexandria ask Rabbi Yehoshua ben Chananya: How does one have male children?  Rabbi Yehoshua’s answer is that “He must marry a woman who is appropriate for him, and sanctify himself (Rashi: with tzeniut) during intimacy.. The Alexandrians respond skeptically: “many have done … but …”.  Their skepticism seems justified, as Rabbi Yehoshua’s answers to their other questions are playful and perhaps even mocking.
Based on this parallel, I suggest that Kimchit’s response to the Sages was tzanua – she meant that she did not uncover her hair even during intimacy.
Men and women each go to extremes of tzeniut in hopes of reward.  As a result, it is clear that the extremes of tzeniut discussed here have nothing to do with a hypothetical male gaze, or for that matter any real or hypothetical human gaze.  The concern is rather for the Divine gaze, that sexuality per se is inherently embarrassing.
Practitioners of extreme tzeniut are constantly sewing figleaves lest G-d come walking through their garden.  Their actions may be profound expressions of fear of G-d, but they are not imitatio dei.  Ultimately, our goal has to be “vehatzaneia lekhet im Elokekha”, walking in tzeniut together with Hashem.