However, "The everlasting Father" does not mean God here, in your theologies.
1. God is Spirit, John 4:24, not flesh and blood and in the OT either spoke directly to the prophets or by angels and also various objects like a burning bush or an ass for example. Between the OT and NT God was silent towards Israel as when they returned to Israel from the Babylonian captivity they came back as merchants and not shepherds as they were disobedient to God going after other gods, Book of Malachi.
2. Jesus being the very Spirit of God before the foundation of the world as He and the Father are one was prophesied by the Prophets in the OT and spoken of by John the baptist in the NT as John being the forerunner of Christ calling all to repent. As foretold Christ did come as the word of God made flesh (skin, bone, blood) to be that light that shines in darkness. He came as redeemer Savior through Gods grace as Christ is our faith that all can repent of their sins and have eternal life with the Father to all who will believe in Him as Lord and Savior. John 1:1-4; 1 Peter 1:13-21
3. After the sacrifice of Christ God raised Him from the grave and as He had to ascend back up to heaven the promise was that He would never leave us or forsake us as when He ascended He sent down the Holy Spirit (Spirit of God) to indwell all who will believe in Christ and His finished works on the cross. In the OT Gods Spirit fell on them for a time and purpose under heaven. Now we are indwelled with that power and authority through Gods grace that the Holy Spirit now works in us and through us teaching all things God wants us to learn. All three are Spiritual and Spiritual awakenings in us to know the will of God and walk in His statures. John 16:7-15
Ephesians 4: 5 One Lord, one faith, one baptism, 6 One God and Father of all, who is above all, and through all, and in you all.
1 John 5:6 This is he that came by water and blood, even Jesus Christ; not by water only, but by water and blood. And it is the Spirit that beareth witness, because the Spirit is truth. 7 For there are three that bear record in heaven, the Father, the Word (Jesus), and the Holy Ghost: and these three are one. 8 And there are three that bear witness in earth, the Spirit, and the water, and the blood: and these three agree in one.
God the Father, God the Son, God the Holy Spirit as all three coequal Gods Spirit.
Jesus being the right arm of God who knew no sin. Isaiah 53:1 Who hath believed our report? and to whom is the arm of the LORD revealed? 2 For he shall grow up before him as a tender plant, and as a root out of a dry ground: he hath no form nor comeliness; and when we shall see him, there is no beauty that we should desire him. 3 He is despised and rejected of men; a man of sorrows, and acquainted with grief: and we hid as it were our faces from him; he was despised, and we esteemed him not.
Jesus is the word of God. John 12:49 For I have not spoken of myself; but the Father which sent me, he gave me a commandment, what I should say, and what I should speak. 50 And I know that his commandment is life everlasting: whatsoever I speak therefore, even as the Father said unto me, so I speak.
Jesus is word, light and life that is God come in the flesh. John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 The same was in the beginning with God. 3 All things were made by him; and without him was not any thing made that was made. 4 In him was life; and the life was the light of men.
Gods Holy Spirit has come to indwell us and teach us. John 14: 26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
Just like the word Trinity you are not going to find the exact words "God Holy Spirit" written in scripture, but scripture explains there is only one God, not three, as God exist in three persons, Father, Son and Holy Spirit. All three are each God, meaning equal in power, nature and attributes and worthy of the same praise. This doesn't mean there are three gods as there is only one true God. It also doesn't mean that these are different forms of God as each is its own person. It's hard to wrap our heads around this as we can not fully understand God.
The Holy Spirit appears in both the OT and NT. In Genesis 1:2 the Spirt of God was hovering over the waters. In Genesis 1:26 Let us make mankind in our image. The word "us" means God, Son Jesus and Holy Spirit (Trinity=3) all being before the creation of the world.
The Holy Spirit has power and emotions and is active among His people. Isaiah 63:10 But they rebelled, and vexed his Holy Spirit (God Holy Spirit). Nehemiah 9:20 Thou gavest also thy good spirit to instruct them, (God Holy Spirit). Now under the dispensation of God's grace we have God, Jesus and the Holy Spirit dwelling in us as we are all one in Him and He in us through that of the Spiritual rebirth from above, John 3:5-7; Acts chapter 2; 1 John 4:12-17.
Scriptures that reference Jesus being referred to as God:
John 1:1-14; John 10:30; Romans 9:5; Colossians 2:9; Hebrews 1:8, 9; 1 John 5:7, 8, 20; 1 Corinthians 8:6; 2 Corinthians 3:17; 13:14; Isaiah 9:6; 44:6; Luke 1:35; Matthew 1:23; 28:19; John 14:16, 17; Genesis 1:1, 2 (cross reference John 1:1-14); 1 Corinthians 12:4-6; Ephesians 4:4-6; Colossians 1:15-17; John 14:9-11; Philippians 2:5-8; Rev 1:8
Scriptures that reference the Holy Spirit as being God:
Psalms 139:7, 8; John 14:17; 16:13; Isaiah 40:13; 1 Corinthians 2:10, 11; Zechariah 4:6; Luke 1:35; Ephesians 4:4-6; Romans 5:5; 1 Corinthians 6:19; Ephesians 1:13; 1 Thessalonians 1:5; Titus 3:5; 2 Peter 1:21; Jude 1:20