Several Church Fathers refer to the Holy Spirit as feminine, often citing now-lost [Gospel of the Hebrews](https://www.earlychristianwritings.com/text/gospelhebrews-ogg.html), in which Jesus speaks of "My Mother, the Holy Spirit." Origen quotes from it thus:

> And if any accept the Gospel of the Hebrews - here the Savior says:
> "Even so did my mother, the Holy Spirit, take me by one of my hairs and
> carry me away on to the great mountain Tabor..."  If the name of brother of Christ may be applied, not only to the race of men but to beings of diviner rank than they, then here is nothing absurd in the Holy Spirit's being His Mother; everyone being His mother who does the will of the Father in heaven.
> (Origen, Commentary on John 2.12.87 [on John 1:3])

Jerome also cites this Gospel. In his Commentary on Isaiah, he writes:

> "The eyes of a maid look to the hand of her mistress" [Ps. 123:2] The
> maid is the soul and the mistress (*dominam*) is the Holy Spirit. For
> also in that Gospel written according to the Hebrews, which the
> Nazaraeans read, the Lord says: 'Just now, my Mother (*mater*), the Holy
> Spirit, took me.' *Nobody should be offended by this, for among the
> Hebrews the Spirit is said to be of the feminine gender*, although in our language it is called to be of masculine
> gender and in the Greek language neuter. (Jerome, Commentary on Isaiah
> 11, 40, 9 - Adriaen 1963:459)

This lost Gospel of the Hebrews [may or may not be heretical](https://en.wikipedia.org/wiki/Gospel_of_the_Hebrews). The fact that several Church Fathers cite it in a positive context shows that there is a church-historical basis for the idea of the Holy Spirit being what the OP call an "Eternal Matriarch."

Several other church-historical references to the Holy Spirit's femininity are cited in ["The Holy Spirit as feminine: Early Christian testimonies and their interpretation"](http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0259-94222016000100026) by Johannes van Oort.

**The above early Church Fathers departed from the traditional view that the Holy Spirit can only be considered male -- the masculine agent that conceived Jesus in Mary's womb. They were willing to consider and not be offended by the idea the the Holy Spirit is feminine, the heavenly counterpart to his earthly mother, Mary.**