When Joseph recorded his “first vision” he never mentioned The Holy Ghost in any of the versions published. See all of the accounts side by side.

It no sooner appeared than I found myself delivered from the enemy which held me bound. When the light rested upon me I saw two Personages, whose brightness and glory defy all description, standing above me in the air. One of them spake unto me, calling me by name and said, pointing to the other—This is My Beloved Son. Hear Him! (JS-H 1:17)

Why didn’t Joseph see the Holy Ghost? It is a witness of the Father and the Son. (2 Nephi 31:18), (D&C 20:27), (3 Nephi 28:11).

I was taught that the Holy Ghost is a personage AND a member of the Godhead.

“This is the office of the Holy Ghost, who is a personage of spirit, one of the trinity of the Godhead. It is his mission and office to bear witness of the Father and of the Son and of the truth of all things.” – George F. Richards (CR Oct 1931)

While the Holy Ghost may be conferred upon us, and is designed to be our guide and support, it is only restrained and manifested in its fulness in our guidance and defense in proportion to the degree to which we cultivate it and listen to its promptings. We may lose it entirely through indifference or transgression and once deprived of its presence we are left in darkness more dense than before its reception. Cultivate it, my brethren and sisters, and it will become in reality the iron rod, which is the word of God, and will lead us back to him. – Anthony W. Ivins (CR Apr 1934)

That by keeping the commandments they  might be washed and cleansed from all their  sins, and receive the Holy Spirit by the laying on of the hands of him who is ordained  and sealed unto this power. – Melvin J Ballard (Three Degrees of Glory)

“Elder James E. Talmage taught: “That the Spirit of the Lord is capable of manifesting Himself in the form and figure of man, is indicated by the wonderful interview between the Spirit and Nephi, in which He revealed Himself to the prophet, questioned him concerning his desires and belief, instructed him in the things of God, speaking face to face with the man. . . . However, the Holy Ghost does not possess a body of flesh and bones, as do both the Father and the Son, but is a personage of spirit.” (1 Nephi 11:11)

“The chief agent or agency by which the Holy Ghost accomplishes his work is usually spoke of as the Holy Spirit or the Spirit of God. It is a universe-filling medium or influence.” (John A. Widtsoe, Evidences and Reconciliation’s, (3 volumes in one), 1962, p. 62).

“The Holy Ghost is the third member of the Godhead. He is a Spirit, in the form of a man.” – Joseph Fielding Smith

So he should have seen him too according to our present teaching and understanding on the Godhead taught in church manuals such as the Doctrines of the Gospel Manual.

“The Father has a body of flesh and bones as tangible as man’s; the Son also; but the Holy Ghost has not a body of flesh and bones, but is a personage of Spirit. Were it not so, the Holy Ghost could not dwell in us.” (D&C 130:22)

The Holy Ghost is yet a spiritual body and is waiting to take to himself a body, as the Savior did.” [Joseph Smith, Encyclopedia of Joseph Smith’s Teachings, edited by Larry E. Dahl and Donald Q. Cannon (Salt Lake City: Bookcraft, 1997)]

If we look at Stephen’s experience, he saw two personages as well, and it’s described that he was filled with the Holy Ghost.

But he, being full of the Holy Ghost, looked up steadfastly into heaven, and saw the glory of God, and Jesus standing on the right hand of God, And said, Behold, I see the heavens opened, and the Son of man standing on the right hand of God.” (Acts 7:55–56)

This is all leading to The Lectures on Faith, particularly Lecture 5.

Why did Joseph teach that the Godhead consisted of TWO personages, and not THREE personages?

“There are two personages who constitute the great, matchless, governing and supreme power over all things—by whom all things were created and made, that are created and made, whether visible or invisible: whether in heaven, on earth, or in the earth, under the earth, or throughout the immensity of space—They are the Father and the Son:

Question 3: How many personages are there in the Godhead?
Two: the Father and the Son.” (LOF 5:2)

He says the Godhead consists of three, but only two are personages.

We shall, in this lecture speak of the Godhead: we mean the Father, Son and Holy Spirit.

And he being the only begotten of the Father, full of grace and truth, and having overcome, received a fulness of the glory of the Father—possessing the same mind with the Father, which mind is the Holy Spirit, that bears record of the Father and the Son, and these three are one, or in other words, these three constitute the great, matchless, governing and supreme power over all things: by whom all things were created and made, that were created and made: and these three constitute the Godhead, and are one:

Why doesn’t he say the Holy Spirit is a personage? Could it be that The Holy Ghost and The Holy Spirit are different? It’s interesting that D&C 76 doesn’t mention The Holy Ghost one time, yet we’ve assumed it does. Is this important? D&C 130:22 doesn’t say Godhead either, but we assume that’s what it’s teaching.

Let us here observe, that three things are necessary, in order that any rational and intelligent being may exercise faith in God unto life and salvation. First, The idea that he actually exists. Secondly, A correct idea of his character, perfections and attributes. Thirdly, An actual knowledge that the course of life which he is pursuing, is according to his will.—For without an acquaintance with these three important facts, the faith of every rational being must be imperfect and unproductive; but with this understanding, it can become perfect and fruitful, abounding in righteousness unto the praise and glory of God the Father, and the Lord Jesus Christ.” (LOF 3:2-5)

I’ve intentionally included quotes about the Holy Ghost, Holy Spirit, and Godhead by the following persons, “George F. Richards, Anthony W. Ivins, Melvin J. Ballard, James E. Talmage, John A. Widstoe, and Joseph Fielding Smith.” These men disagreed with Joseph Smith about the nature and character of the Godhead. As a committee in 1921 they took out the Lectures on Faith, known as the “Doctrine” portion of the Doctrine and Covenants.

This needs to be studied out, and pondered over. Your Faith might depend on it!

“…by proving contraries, truth is made manifest, and a wise man can search out old paths, wherein righteous men held communion with Jehovah, and were exalted through obedience.” – Joseph Smith

Praise to the man who communed with Jehovah.