A Biblical Unitarian understanding is based on there being one God - the Father, and His human son Jesus. The spirit is the presence and power of God for good in all things.
Jesus replied, "Anyone who loves me will obey my teaching. My Father will love them, and we (the Father and Jesus) will come to them and make our home with them.
How does Jesus and the Father do this?
I will ask the Father, and He will give you another helper, so that He may be with you forever; 17 the Helper is the Spirit of truth, whom the world cannot receive, because it does not see Him or know Him; but you know Him because He remains with you and will be in you.
18“I will not leave you as orphans; I am coming to you. 19 After a little while, the world no longer is going to see Me, but you are going to see Me; because I live, you also will live. 20 On that day you will know that I am in My Father, and you are in Me, and I in you. John 14:16-20
Jesus is going to be with them - 'coming to them', as is the Father by or through the spirit. This is how God had always operated since the beginning in interacting with His created humans, and now Jesus can also interact through the same spirit of God to be 'present' when he is not literally/bodily here on earth.
Exalted to the right hand of God, he has received from the Father the promised Holy Spirit and has poured out what you now see and hear. Acts 2:33
But the Advocate, the Holy Spirit, whom the Father will send in My name, will teach you all things and will remind you of everything I have told you. John 14:26
"He will give you another helper" - Jesus is the primary paraclete - the spirit is 'another' - to follow up what Christ had begun. Explained here.
the mystery which has been hidden from the past ages and generations; but has now been manifested to His saints. Col 1
That which was from the beginning, which we have heard, which we have seen with our eyes, which we have looked upon, and our hands have handled, concerning the Word of life— 2the life was manifested, and we have seen, and bear witness, and declare to you that eternal life which was with the Father and was manifested to us— 3that which we have seen and heard we declare to you, that you also may have fellowship with us; and truly our fellowship is with the Father and with His Son Jesus Christ 1 John 1:1-3
John explains this 'manifested' mystery. Jesus IS the mystery of God revealed. His plan, word and will are manifested perfectly in Christ. He IS the word, will and plan of God.
Now all believers, current and future have fellowship with God and His son as His spirit and our spirit are drawn into unity.
You, however, are not in the realm of the flesh but are in the realm of the Spirit, if indeed the Spirit of God lives in you. And if anyone does not have the Spirit of Christ, they do not belong to Christ. Rom 8:9
...preach to the Gentiles the unfathomable riches of Christ, 9and to enlighten all people as to what the plan of the mystery is which for ages has been hidden in God, who created all things; 10so that the multifaceted wisdom of God might now be made known through the church to the rulers and the authorities in the heavenly places. 11This was in accordance with the eternal purpose which He carried out in Christ Jesus our Lord Eph 3:8-
insight into the knowledge of the mystery of God, Christ, 3 in whom all the treasures of wisdom and knowledge are hidden Col 2:2
The overwhelming thrust of God's redemption of man through His son is the relationship that they had as Father and son - the desire that we too be one as they are one. This unity is spiritually obtained, not by our human will, but by the presence of God and Jesus within us - His will active in us, as it was in Jesus.
that all of them may be one, as You, Father, are in Me, and I am in You John 17:21
This same connection is evident with Jesus at his baptism. Jesus saw the heavens opened, he saw the spirit animated or manifested as a dove. This was a display for his benefit as well as any others who witnessed this provision of the Father for His son immediately prior to his temptation and beginning of his ministry. The Father dwelt in Jesus through His spirit. Just as He and Jesus do in believers now, until the end of the age.
After He was baptized, Jesus came up immediately from the water; and behold, the heavens were opened, and he saw the Spirit of God descending as a dove and settling/resting on Him Matt 3:16