John 15:26 says the Paraclete “proceeds from the Father”, not “the Father alone”. The Paraclete proceeds not only from the Father, but also the Son (see John 14:26/16:7).
To conceive of God comparisons to created beings must not be made. God is not compared to. He is. In being there is everything, but being has no body, and the eternal Being has no body.
Look: God is light. This is the only thing that can represent God without being antithetical to His spiritual Essence. The light exists, and yet it is incorporeal. You see it, but you cannot touch it. It exists.
Their Trinity is light. And unbounded light. The Source of Itself, living by Itself, and acting in Itself. The universe’s greatness does not equal its Infinity. Its essence fills the Heavens, glides over creation, and holds sway over the infernal caverns. It does not penetrate you — that would be the end of Hell — but it overwhelms them with its glowing, which is beatific in Heaven, comforting on Earth, and terrifying in Hell. Everything is threefold in them (the Trinity). Forms, effects, and powers.
God is light. A vast, majestic, and peaceful light is given by the Father. An infinite circle which has embraced all Creation since the moment when “Let there be light” was said until forever and forever for God, who existed and will continue to embrace all that — in the final form, the eternal one, after the Judgement — will remain in Creation. He will embrace those are eternal with Him in Heaven.
Within the eternal circle of the Father there is a second circle, begotten by the Father, working differently, and yet not working in contrary fashion, for the Essence is one. It is the Son. His light, more vibrant, not only gives life to bodies, but gives Life to souls that had lost it by means of His sacrifice. It is a flood of powerful, gentle rays which nourish your humanity, and instruct your mind.
Within the second circle, produced by the two workings of the first circle, there is a third circle with even more vibrant, inflamed light. It is the Holy Spirit. He is the Love produced by the relations of the Father and the Son, the intermediary between the Two, and a consequence of the Two, the wonder of the wonders.
Thought created the Word, and Thought and Word love one another. Love is the Paraclete. He acts upon your spirit, your soul, and your flesh. For He consecrates the whole temple of your person, created by the Father and redeemed by the Son, created in the image and likeness of the Triune God: the soul. The Holy Spirit is the chrism upon the creation of your person, made by the Father; He is grace to benefit from the Sacrifice of the Son; He is Knowledge and Light to understand the Word of God. A more concentrated Light, not because it is limited in comparison to the others, but because it is the spirit of the spirit of God, and because, in its condensation, it is most powerful, as it is most powerful in its effects.
That is why Jesus said, “When the Paraclete comes, He will instruct you” (John 14:26). Not even, Jesus, who is the Father’s Thought that has become the Word, can make you understand what the Holy Spirit can make you understand with a single flash.