It seems that there has been some development of statements (I wont say Tradition) about the Holy Spirit. The Creed was expanded to say that He proceeds from the Father and is worshiped and glorified with the Father and the Son, but still does not go into the same detail as it does the Son. Rublev’s icon of the Trinity, or the Hospitality of Abraham, portrays the Holy Spirit as being as much of a person as the Father and the Son. There are more vague statements made of Him however. Olivier Clement includes these:
The very name of Christ is a Trinitarian name: Christos, Messiah, means ‘anointed’ with the Messianic unction. Now the Father is the one who from all eternity ‘anoints’ the Son by causing the Spirit to rest on him, or rather in him, as an unction, the ‘oil of gladness’ of the psalm, because the Spirit is the joy of the divine communion.
To name Christ is to confess the whole, for it is to point to God (the Father, the ‘principle’ of the godhead) who has anointed the Son; and to the Son who has been anointed, and to the unction itself, which is the Spirit. This accords with Peter’s teaching in Acts: ‘God anointed Jesus of Nazareth with the Holy Spirit’ (Acts 10:38) and with the teaching of Isaiah: ‘The spirit of the Lord is upon me, because the Lord has anointed me’ (Isaiah 61:1), The Psalmist simply says, ‘Therefore God, your God, has anointed you with the oil of gladness’ (Psalm 45:7).
Basil of Caesarea On the Holy Spirit, 12 ( The Roots of Christian Mysticism p. 59)
This next passage makes Him sound more like a Person, but yet seems to set Him apart (not a good word, but the distinction seems more) from the Father and the Son.
That God is, and that he is everywhere and fills the universe, is known by the angels and the saints who have purified themselves, because they are enlightened by the Holy Spirit. But where, how, and what he is, not one amongst all beings knows: only the Father knows the Son and the Son the Father, and the Holy Spirit knows the Father and the Son, since he is co-eternal and identical with them in essence. Indeed these Three who are only One know themselves, and are known by one another. As he himself said who is by nature God and Son of God, ‘Who knows a person’s thoughts except the spirit of a person which is in him? So also no one comprehends the thoughts of God except the Spirit of God’ (1 Cor. 2:11). And again: ‘No one knows the Son except the Father, and no one knows the Father except the Son and any one to whom the Son chooses to reveal him’ (Matthew 11.27).
Diadochus of Photike Catechesis, 5
The following hymn, rising at once to the mystery of the divine cosmic Logos, glorifies in a single sequence the Father as the principle of the godhead, and the Spirit as the ‘bond of the Son and the Father’. [Synesius of Cyrene Hymns, 5] But this bond is himself a Person; nothing in God can be impersonal. (p. 59,60)
[…] The Old Testament has manifested the Father clearly, the Son only dimly. The New Testament has revealed the Son and implied the divinity of the Spirit.
Today the Spirit lives amongst us and makes himself more clearly known. It would actually have been dangerous openly to proclaim the Son while the divinity of the Father was not fully acknowledged, and then, before the divinity of the Son was accepted, to add as it were the extra burden of the Holy Spirit … It was more fitting that by adding a little at a time and, as David says, by ascending from glory to glory, the splendour of the Trinity should shine forth progressively.
Gregory Nazianzen Fifth Theological Oration, 31, 26 (p. 61)
Here’s a new explanation of the Spirit,
The Trinitarian revelation is implicit also in the prayer which Christ himself taught us, the Lord’s Prayer, of which the first three petitions invoke the three divine Persons. For the Son is the Father’s eternal name, which he hallowed to the point of death on a cross. And the Kingdom is identified with the Spirit, who is therefore both the unction of the Son and the Kingdom of the Father, as Paul Florensky observed.
Our Father, who art in heaven,
Hallowed be thy name,
thy Kingdom come.
By these words the Lord is teaching those who pray to begin with the very mystery of God … The words of the prayer really point to the Father, the Father’s name, and the Kingdom, to teach us … to honour, to call upon and to adore the One Trinity. For the name of God the Father, in its essential subsistence, is the only-begotted Son. And the Kingdom of God the Father, is the essential subsistence, is the Holy Spirit. For what Matthew calls ‘Kingdom’ another evangelist calls Holy Spirit: ‘Thy Spirit come…’ (Luke 11.2 variant reading).
Maximus the Confessor Commentary on the Lord’s Prayer (p.62)