There were ceremonies in the Old Temple that were not necessarily associated with any piece of furniture.
Exodus 40:12-15, "And thou shalt bring Aaron and his sons unto the door of the tabernacle of the congregation, and wash them with water. And thou shalt put upon Aaron the holy garments, and anoint him, and sanctify him; that he may minister unto me in the priest’s office. And thou shalt bring his sons, and clothe them with coats: And thou shalt anoint them, as thou didst anoint their father, that they may minister unto me in the priest’s office: for their anointing shall surely be an everlasting priesthood throughout their generations." Exodus 28:41, "And thou shalt put them upon Aaron thy brother, and his sons with him; and shalt anoint them, and consecrate them, and sanctify them, that they may minister unto me in the priest’s office."
Aaron and his sons were washed, anointed, and clothed in front of "the door of the Tabernacle..." in preparation to function as priests who were clean and worthy to perform ordinances.
Life and Light
Anointing symbolizes or implies the addition of life to something (see 2 Chron. 23:11, 1Kings 1:34, 2Kings 11:12), the same way blood represents death. The cell membranes in our bodies are composed of a phospolipid bilayer, made up of fat similar to that found in olive oil. (Incorporating monounsaturated fat from olive oil into a cell membrane improves the function of various receptors by loosening densely packed saturated fat molecules.) The molecules are literally life itself. Olive oil is a cure for more poisons than any other known substance. It fuels the seven lamps of the Menorah. The symbolic intersection of life and light is olive oil. And olive oil is used to anoint kings (like David; see 1 Sam. 16:20), as well as the priests working in the Old Temple. It is associated with coronation outside the Temple, as well as priestly devotion within.
Anointing Him
"Christ" and "Messiah" both mean "The Anointed One." Jesus is anointed by a woman in all four gospels. There was controversy surrounding the event. One possible reason is that pouring oil on someone's head is equivalent to casting a ballot for their kingship, ergo, AGAINST the current king—in other words, an act of treason and revolution. Judas goes to the leaders immediately after this event (Matt. 26:6-14). This may have been the context for Jesus' remark about His burial in verse 12. If the recipe of the mixture poured on Jesus were the same as that used in the Temple, it would have also constituted an offense in the eyes of the some, punishable by expulsion from society (Ex. 30:32-33). The woman also uses her unbound hair to wipe Jesus' feet, a cultural proscription of the time—only a husband could see his wife's unbound hair. This act was potentially offensive on many levels besides the waste of a year's wages worth of ointment that could have been sold to feed the poor (Matt. 26:8-9).
The anointing described in Leviticus and Exodus confirmed that Aaron and his sons were priests. Anointing also confers kingship—David's anointing secured his status as God's choice for king of Israel. Both lines of heritage converged in Jesus; He was related to John the Baptist through Mary. John's parents parents were descended from Aaron (Luke 1:5). Jesus descended from King David as well (Isa. 11:1-5).
Conceptualizing Its Significance
I want to suggest something, a metaphorical parallel between Aaron's anointing and Enoch's dispensation. Enoch and Zion are exemplary of what the Church may become, of what the world will become when Jesus comes again. Enoch's was one of the few communities that got it right. Moses tried to lead the people up the mountain to meet God, but they refused. Brigham Young tried to found a Zion society, and the stubbornness of the people, combined with the arrival of the railroad, blended worldliness back into it. Many have tried, but Enoch actually succeeded in creating a Zion society. This success did not include the whole earth—just his people. But it shows that it is more than a pipe dream. His City of Enoch will come down out of heaven, still in its translated, immortal state, and those righteous people who are left on earth will meet them at the Second Coming. In other words, this earth will be fit to reincorporate Zion.
Just as the Zion of Enoch is a promise of what modern Zion is able to become, so the ordinance of anointing Aaron and his sons prefigures their meeting with God, and their potential to become kings. Remember, this ordinance occurs OUTSIDE the Tabernacle—in proximity to the fallen world we live in, rather than inside the Holy of Holies, the "finish line" of the Temple or Tabernacle. There is still a great deal of work and ceremony between the promise made in the courtyard through anointing, and its ultimate realization
And just as Enoch's city is not on the earth, so there is no visible furniture in the Temple associated with anointing.
Jesus performed the Atonement in a grove of olive trees called Gethsemane. Just as blood was crushed out of Him by the weight of our sins, and became a source of life for us, so the oil crushed out of olives in presses represents that life-conferring power achieved through His suffering, death, and resurrection.
