A short tidbit from Kol haTor chapter 1, siman bet:
עפ"י רבנו הגר"א כל עבודת קבוץ גלויות, בנין ירושלם והרחבת ישוב אר"י להחזרת השכינה
According to our Rabbi, the GR"A, all of the work of ingathering of the Exiles, building of Yerushalayim, and expanding the settlement in Eretz Yisrael is (in order to bring) the return of the Shechinah.
In tandem with this, we have that this work begins at the beginning of the first hour in 5500. Putting this together, this appears to confirm what I wrote before; the 24 hour division in Kol haTor comes to explain the GR"A's words in Sifra diTzniuta regarding the correlation in time between the tikkunim Above and the events below. The Nesirah brings the return of the Shechinah to Tzion.