The main means by which St. Ambrose sets about demonstrating the divinity of the Holy Spirit in the first several chapters of the second book of his treatise On the Holy Spirit is to show how the Father, the Son and the Holy Spirit are one. To do this, he shows that titles given to the Father and/or the Son are also given to the Holy Spirit. This from chapter two:
For the Spirit Himself is Power, as you read: ‘The Spirit of Counsel and of Power (or might)’ (Isa. 11:2). And as the Son is the Angel of great counsel, so, too, is the Holy Spirit the Spirit of Counsel, that you may know that the Counsel of the Father, the Son, and the Holy Spirit is One.
One of the connotations of the Greek word βουλή (counsel) is the process or deliberation by which a decision is made or a problem is resolved. In terms of a royal court, this process would include a small, trusted inner group of counsellors that the king would turn to in order to get advice.
Thus, the implication of giving the title Counsel to God is that He wishes us to be part of that inner group — part of that process. It is not His will to rule from on high and arbitrarily judge His creation. Rather, He willingly descends into the mire and muck that is the fallen world in order to raise us up into that heavenly court. As we sing in the Kontakion of the Forefeast of Christmas:
On this day the Virgin comes to a cave to give birth to God the Word ineffable, Who was before all the ages. Dance for joy, O earth, on hearing the gladsome tidings; with the Angels and the shepherds now glorify Him Who is willing to be gazed on as a young Child Who before the ages is God.
How awesome is the mystery that God so loves us — that God so desires us to be part of his inner and trusted circle — that He would send us His Son to become a babe.