On the one hand, the Jehovah's Witnesses are quite right: Greek grammar does not support the translation of "he" for the Holy Spirit. The passages you mentioned in John do not actually use the masculine pronoun to refer directly to the Holy Spirit. I published an article on this in 2003 in the Bulletin of Biblical Review. It's called "Greek Grammar and the Personality of the Holy Spirit." Now, that's on a grammatical level.
But the JWs take this beyond the evidence by saying that since the grammar doesn't support the personality of the Holy Spirit, there is nothing else that does. In this case, I believe they are quite wrong. Gender in Greek is primarily an arbitrary thing; that is, it does not necessarily have to do with "natural gender" or whether someone/something is masculine, feminine, or neuter. For example, the word "word" in Greek is masculine, though there is also a word for "word" which is neuter. The word "child" in Greek is neuter. And this word is used of Jesus as a baby. Does this mean that he was an "it" until he grew up? Hardly. This is actually similar to some modern languages. Thus, for example, in German the word for girl is neuter. This certainly does not mean that Germans think of girls as "things"! What's interesting is that the Hebrew word for "Spirit" is feminine. Since that is the case, why don't JWs say that the Holy Spirit is a person, a female person? They are highly selective in the data, and they simply refuse to listen to genuine arguments when it doesn't support their case.
Now, how would I argue that the Holy Spirit is a person? I believe that the very passage that many use to describe the Spirit as a person (John 14-16) contains the key. Although the Greek does not do so via grammatical gender, there are other ways to see the personality of the Spirit here. For example, Jesus says that the Father will send "another advocate/comforter" (John 14.16; cf. also 14.26; 15.26; 16.7-8). If he is "another" advocate then he is distinct from Jesus. Yet, clearly, he is sent to replace Jesus as the one who ministers to the disciples. How can a thing do this? In the Upper Room Discourse (John 14-17) the Holy Spirit is seen as (a) distinct from the Father and the Son, and (b) personal. He will teach, guide, etc. These are attributes of persons, not things. Also, in the Great Commission, Jesus tells his disciples to "baptize in the name of the Father, of the Son, and of the Holy Spirit." Now, what's curious here is the subtle equation of the Son with the Father, and the Spirit with the Father. No one would think of saying, "Baptize in the name of the Father and the Bible," or even "the Father and Paul." The first expression is something that we have a reaction to because the Bible is inanimate. These second expression is something that we have a reaction to because it places Paul on the same plane with God. What's remarkable about the wording of the Great Commission is that (a) the Greek does not make the Father, Son, and Holy Spirit the same person, but (b) it does make them equal.
One question that I believe most Christians do not wrestle with, and that the article I wrote is addressing, is this: Why is it that the New Testament doesn't say more about the personality and deity of the Holy Spirit? I think the reason is that it took some time for the apostles to come to grips with this fact. Up until the time of the New Testament, the Spirit was viewed either as God's alter ego, or simply his spirit (just like each of us has a spirit), or as a force, especially as a liquid. When Genesis 1.2 says that "the Spirit of God was moving over the surface of the water" we cannot read this text as though Moses understood the Trinity! In Acts 2, when Luke tells us that the Spirit was poured out on the apostles on the day of Pentecost so that each apostle was "filled with the Spirit" the language seems to suggest that the Spirit was a liquid. Yet, Luke also says that "they began to speak in other languages as the Spirit enabled them" (Acts 2.4). That certainly seems like more than what a liquid can do! My take on things is that the apostles wrestled with who and what the Spirit was for some time. They were like blind men feeling an elephant: Each man describes a different part of the elephant, but no one has a full impression of it. So it is with the New Testament writers. It has been the task of the church to put the pieces together in a way that satisfies all the data. Jehovah's Witnesses are also like blind men feeling an elephant, except that they don't feel every part of the elephant. Consequently, their picture is marred. The Council of Chalcedon (AD 451) put together the pieces in a way that accurately describes who and what the Spirit is, and it did so by explaining ALL of the parts.