In no particular order, here is the result of some studying. I throw them out as thoughts for contemplation, dialogue, and prayer, not conclusions.
Thoughts from or provoked by Matthew Henry. . .
from commentary on John 16:7-15
The Holy Spirit came in answer to "Christ's intercession within the veil." His role in the Christian life is a direct result of the tearing of the veil. This seems to support a more obvious and universal application of the Spirit under the new covenant than in the Old Testament, as postulated in my previous ramblings.
The Holy Spirit "will convince the world concerning sin, righteousness, and judgment." Here's a new idea. The Holy Spirit takes the place of the law (see Roman 3:20). In the commentary on Acts 2, Henry points out that the first outpouring of the Holy Spirit takes place at Pentecost--the Jewish holiday celebrating the giving of the law on Mount Sinai. Jesus was crucified during the Passover celebration. . .the sacrifice for salvation in the new covenant. The Holy Spirit was given during Pentecost. . .the law of the new covenant. It makes sense. Jump to Romans. . .
from commentary on Romans 8:1-9
OT law was a covenant of works; the new law of the Spirit is a covenant of grace. We are therefore free from the law of sin and death and now under "the law that gives the Spirit, spiritual life to qualify us for eternal." The requirement for satisfaction after a breach of law is satisfied by imputing Christ's righteousness to us. The requirement for obedience to the law is satisfied by the Spirit writing the law of love on our hearts; love is the fulfillment of the law.
The Spirit dwells in the sanctified believer, but only visits the unregenerate. Old Testament believers were not sanctified? Only after Christ's sacrifice could man be considered sanctified and therefore able to be a temple of the Holy Ghost.
The Holy Spirit in our lives is the Spirit of God motivating us to conform to the Spirit of Christ. He is somehow a reflection of the other two persons, yet still separate Himself.
from commentary on Romans 8:10-16
We cannout please God without the Spirit, but the Spirit will not work without our own corresponding effort. We are "led" by the Spirit as rational beings, but not "driven" as cattle.
from commentary on Acts 11:1-18, 10:44-48
The Holy Ghost is the gift of Christ, sent after He left His disciples. Does this make it separate from water baptism? All of the disciples would have been water baptized around the time that Jesus was, possibly by John the Baptist. Either the Spirit's baptism was delayed for only the disciples because of their unique position in time, living and experiencing Christianity parallel to Christ, or it is a separate thing from water baptism.
MH says the Holy Spirit is a "kind of baptism." For the first Christians, the Jews, it was a kind of confirmation after water baptism. God gave the Holy Spirit to the Gentiles as a way of showing His acceptance of their repentance. It was necessary that it happen before water baptism, because Peter would not have allowed the Gentiles to experience water baptism without the evidence of Spirit baptism. The baptism of the Spirit proved to the Jewish believers that the Gentiles were worthy of water baptism. It was still necessary, because we are tied to physical ordinances, even though God, of course, is not. Peter argued for the Gentiles' water baptism, saying (according to MH's translation), "Can we deny the sign to those who have received the thing signified?" This seems to mean that the external sign of water baptism is a physical seal of Christian fellowship and acceptance of new believers, the physical symbol of the spiritual seal given through the Holy Spirit.
Thoughts from Augustine. . .
The Holy Spirit is the "admonitio" to return to divine Truth. "Admonitio" is a "reminding" or a "friendly admonition." He is a gift. He is fully divine, by reason of the Scripture saying our "bodies are the temples of the Holy Spirit." As a temple is a structure fit for deity alone, the Holy Spirit is deity. (I know this is not in dispute; I've simply never heard this support before and thought it worth mentioning.) In human experience, the Holy Spirit is love. The Trinity--Father, Son, and Holy Spirit--may be described as lover, loved, and love, respectively. The Spirit is the love that unites the Trinity. (I find this description especially intriguing in light of Dr. Thimel's teaching. . .see previous post on the Holy Spirit.) The Father and Son are both "holy" and "spirit" in their individual persons; the Holy Spirit is what they share in common. As the representation of the relationship between the Father and the Son, He is also the relationship between God and the church (the arbiter of or the actual relationship or both?). The Spirit proceeds from God the Father through Christ, so coming from both of them.
Augustine also makes the correlation between Pentecost and Mount Sinai, mentioning the dichotomy between the law of fear written on stone and the law of love written on human hearts by the Spirit. The Holy Spirit, he says, is a "down payment" of the promise, of the believer's inheritance.
Thoughts from Martin Luther. . .
The Father is the Creator. Christ is the Redeemer. The Spirit is the Sanctifier. He is how we are to become "holy and pure and live and continue to be pure." The Spirit does this by leading us into the holy, catholic church. He preserves, preaches, and brings us to Christ through the church. He finishes the work of sanctification through the resurrection of believers after mortal death. The Spirit is bestowed upon the believer at the believer's baptism to do the work of sanctification.