In other words, "the Spirit of truth" will take up residence. Do we have God the Son and God the Father running around inside of us? No. The mind of God, the Spirit of God, is in us, residing in us. It has taken up residence, and therefore the Father is there, as well as the Son.
The apostles were literally seeing the Holy Spirit of God, the essence of God's mind, in the action, in the life, of a fellow human being—Jesus Christ. He was the literal Word of God. He was with them, teaching, leading, guiding them into truth. He was truth personified. His word is truth (John 17:17). His word is spirit (John 6:63). They could literally, directly, see Him and hear Him, the Son of God, which is why He said the Holy Spirit was with them. It, the essence of God's mind, was in Him. What they witnessed with their eyes and ears was being fed directly into their minds, becoming part of their experience.
The Spirit, the essence of God's mind, was on the verge of residing in them, but it was not yet firmly lodged in them where it would consistently manifest the characteristics of the God Family. This is why Luke 24:49 says, "Tarry in Jerusalem until you are endued with power from on high." Power to do what? To submit to the will of God. He gave them the power to keep God's law in the spirit, not just its letter. Any human being with enough willpower can keep the law of God in the letter, but God must empower us to keep it in the spirit. We need more power than what we humanly have to keep God's law in the spirit. God is looking for people who will worship Him in spirit and in truth (John 4:24), and He has empowered us to do that by His Spirit.
John W. Ritenbaugh
The Holy Spirit and the Trinity (Part Five)