This is why Pentecost is such an essential festival in the life of the Church, not because the Spirit needs a day of fame and recognition after years of neglect, but because the Spirit cannot help but fix our faith, mind, hope and love upon Christ Crucified and the Father through whom he is sent to call, gather, enlighten and sanctify the whole Christian Church on earth. This was the promise of the Ascension. "I am going to the Father...and I will ask the Father, and he will give to you another Paraclete (not parakeet), to be with you forever, even the Spirit of truth...he dwells with you and will be in you...he will teach you all things and bring to your remembrance all that I have said to you...when the Paraclete comes, whom I will send to you from the Father, the Spirit of Truth...he will bear witness about me, and you also will bear witness, because you have been with me from the beginning" - John 14-16.
Earlier in Mere Christianity, Lewis had written that the third Person, who is in fact a real Person, grows out of the joint life of the Father and the Son.
"And now, what does it all matter? It matters more than anything else in the world. The whole dance, or drama, or pattern of this three-fold Personal life is to be played out in each of us: or (putting it the other way around) each one of us has got the enter that pattern, take his place in that dance. There is no other way to the happiness for which we are made. Good things as well as bad, you know are caught by a kind of infection. If you want to get warm you must stand near the fire: if you want to be wet you must get into the water. If you want joy, power, peace, eternal life, you must get close to, or even into, the thing that has them. They are not a sort of prize which God could, if He chose, just hand out to anyone. They are a great fountain of energy and beauty spurting up at the very centre of reality. If you are close to it, the spray will wet you: if you are not, you will remain dry. Once a man is united to God, how could he not live forever? Once a man is separated from God, what can he do but wither and die?
...Now the whole offer which Christianity makes is this: that we can, if we let God have His way, come to share in the life of Christ. If we do, we shall then be sharing a life which was begotten, not made, which always has existed and always will exist. Christ is the Son of God. If we share in this kind of life we also shall be sons of God. We shall love the Father as He does and the Holy Ghost will arise in us. He came to this world and became a man in order to spread to other men the kind of life He has - by what I call 'good infection'. Every Christian is to become a little Christ. The whole purpose of becoming a Christian is simply nothing else." - Mere Christianity, Book IV, chapter IV.
All of this is what Pentecost means for us, the Church, Christ's holy people. For what Jesus promised his disciples before Pentecost he now promises - even pours out like a mighty rushing river upon - his entire Church because of Pentecost. Man united with God by the incarnation, by Jesus' death and resurrection and the anointing of the Spirit - all of which churn through the flood gates of Baptism, uniting us with God. What begins with joint divine life in the divine mystery of the Trinity is given to his people through water and Word. Your Baptism is also your Pentecost where you are anointed into paradise and drawn into eternal life as the Triune Name is placed upon you. This is how Lewis' question - How is it possible for us to be taken into the three-Personal life?- is answered. Pentecost, Baptism - in other words, Father, Son and Holy Spirit poured out upon us, filling us with the very life and salvation that comes to us by that same Triune Name. This Pentecost we remember this third Person - this comforter of priceless worth - who makes our hearts his place of rest, pointing us to the Son. What blessed, supernal, infectious joy: the Holy Spirit takes a nose dive into the font and, like a lion, comes bounding into our lives forever.
O Spirit, who didst once restore
Thy Church that it might be again
The bringer of Good News to men,
Breathe on Thy cloven Church once more,
That in these gray and latter days
There may be those whose life is praise,
Each life a high doxology
To Father, Son, and unto Thee.
- LSB 834:4