David Fullmer provides an account of the second anointing.
David Fullmer, "A Brief Sketch of the Life of Dvid E. Fullmer and his Father Peter Fullmer," in Fullmer Family Notebook (ca. 1927), 41, Church History Library, MS 939
When the upper story of the Temple in Nauvoo was finished I received with my companions our washings & anointings and endowments and all ordinances and blessings of the fulness of the Melchesidic Priesthood was confered upon us in which our hearts rejoiced.