This appears to be a variant1 of "קדרותא דצפרא" (the blackness of morning), which is an expression found in the Zohar (e.g. Vayishlach 170a, English translation by Prof. Daniel Matt).
The idea you mention is expressed by the Zohar there (per emended2 translation linked above):
Everyone asks, Who is this looking forth like the dawn? - at first the blackness of morning, then a subtle glow; then fair as the moon, then bright as the sun, then awesome as bannered hosts (Song of Songs 6:10) - beaming powerfully, intensely, fittingly.
Come and see: When day is still dark and concealed, light advances little by little until spreading fittingly. For when the blessed Holy One will arouse to illumine Assembly of Israel, He will glow at first like the dawn, which is black;208 then fair as the moon, then bright as the sun, then awesome as bannered hosts, as has been said. [170b]
Come and see: When morning rises - because it is not written for dawn has come, but rather has risen (Genesis 32:27),209 since when dawn has come, that prince210 is empowered and strikes Jacob, because that hour is black, its potency empowering Esau. Once that blackness of dawn rises, like appears and Jacob is empowered, for then is his time to shine.
208 "like the dawn, which is black The darkness preceding dawn. Rabbi Yehudah is playing on שחר (shaḥar), 'dawn,' and שחור (shaḥor), 'black.'"
209 "has risen The full clause reads: Let me go, for dawn has risen!"
210 "that prince Samael, Esau's heavenly prince, who wrestled with Jacob. See Tanḥuma, Vayishlaḥ 8; Bereshit Rabbah 77:3; Zohar 1:146a, 166a, 170a."
Since you edited your question to ask specifically about a reference to the Vilna Gaon, I'll note that The Wisdom in the Hebrew Alphabet cites "Vilna Gaon, Avnei Eliyahu." Here's the full and precise quote from the book (p. 226):
Jewish History is filled with the experience that periods of darkness and oppression are followed by periods of light and relief. This is similar to what the Zohar describes as: "קַרְדְנוּתָא דְּצַפְרָא," the deep darkness from which daylight emanates. For this reason, the word for morning, שַׁחַר, is related to שָׁחוֹר, black, because the moment immediately preceding the dawn is the blackest period of the night (Vilna Gaon, Avnei Eliyahu).
I think the citation to the Vilna Gaon's Avnei Eliyahu commentary on the Siddur may be mistaken. The actual reference could be to Avnei Eliyahu by R' Eliyahu Frankel (some biographical information here). Avnei Eliyahu doesn't mention the Zohar, and I think Rabbi Michael Munk (author of The Wisdom in the Hebrew Alphabet) was simply trying to reference the concept in the paragraph's first sentence (and perhaps the third sentence) to Avnei Eliyahu. Here is a loose translation of the relevant section of Avnei Eliyahu:
And behold, it is known that the color white represents mercy, and the color black represents judgment, and also night represents judgment. Accordingly, it can be said that this is why the hairs of Rabbi El'azar ben 'Azarya turned white (Mishna, B'rachos 1:5), since he already comprehended what the entire world will understand in future times to come. Namely, that everything is beneficial and merciful.3
And this is the meaning of, "Behold, I am as 70 years old" - since he already appreciated that everything is kindness. And he wanted to bring merit to the public so that the whole world would appreciate this. And this is the meaning of, "And I did not merit that the exodus from Egypt should be recalled at nights" - in other words, even during a time that appears to us to have the attribute of night, we should know that even this is beneficial in the sense of the exodus from Egypt (Mitzrayim), because through the punishment one emerges clean from the distress (meitzer) of sins.
"Until Ben Zoma expounded, as the verse says, 'so that you remember the day that you left the Land of Egypt all the days of your life' (D'varim 16:3), to include even the nights" - in other words, even at a time of judgment, he also knew that it is like the exodus from Egypt. "But the Sages say that this includes the days of the Messiah" - in other words, "all the days of your life" really includes the nights, as Ben Zoma expounded, only that the Sages say that this will be appreciated in the days of the Messiah, and these and those are divrei Elokim chayim. Understand this.
1 For an example of the word variant "קרדנותא" used in this kind of context, see Zohar Chadash (B'reishis, Ma'amar Eser S'firos B'lima, "קרדנותא דסיהרא"). In the particular Zohar passage you reference, the expression is rendered as "קרדנותא דצפרא" in Dagul MeiR'vava by Rabbi Refael Treibish. For more discussion of the usage and meaning of this variant, see Prof. Yehuda Liebes' Chapters of a Dictionary of the Zohar (fn. 51 pp. 167-173).
2 This translation actually omits the relevant words. In the first paragraph on that page, the sentence beginning "Everyone asks" should be emended to: "Everyone asks, 'Who is this looking forth like the dawn?' - at first the blackness of morning (קדרותא דצפרא), then a subtle glow..."
3 See P'sachim 50a (as understood by the Maharsha, Chidushei Agados ad loc.): "אמר רבי אחא בר חנינא לא כעולם הזה העולם הבא העולם הזה על בשורות טובות אומר ברוך הטוב והמטיב ועל בשורות רעות אומר ברוך דיין האמת לעולם הבא כולו הטוב והמטיב ".