First I shall elaborate on this attribute exhibited by many INTJs and then I shall explain what I think are the reasons behind such behavior.
To begin, I think we need to be on the same page here, and therefore I advise everyone interested in this phenomenon to take a look at this three-minute video taken from Waking Life:
YouTube - Telescopic Evolution - Waking Life excerpt Incidentally, my best friend, who is an INFJ, had me watch this video as he told me that this person reminded him of me. In truth, the first time I watched it I was laughing hysterically at how my friend had drew a comparison between this character and myself. I found humor and irony in how animated, idiosyncratic, and passionate the speaker is, but in truth I do exhibit these attributes--particularly if I am inspired and/or talking about something that is of interest to me. I imagine those on vent who have heard me engage in conversation, though a rarity these days, can attest to this. Indeed, I close my eyes at certain points while speaking and my hands move around rhythmically and touch random things at times.
Thus far I have merely expounded on the general observation made by the original poster. It is also important to establish why I, and other INTJs, exhibit this behavior. So I shall establish each piece of the puzzle and then fit it together to form the whole. First, the closing of eyes indicates that the speaker is at that moment highly in tune with his or her inner world of ideas. More specifically, in addition to being broadly in tune when the eyes close it communicates sheer hardcoreness and intimacy with that particular point and how it is so critical to the bigger picture. It is important to remember that for INTJs Ni establishes a broad agenda and Te is used to externalize this agenda and work to bring it to fruition. When the eyes go shut, it is a moment of intellectual ecstacy wherein Ni, Te, and Fi coincide on a point that is critical to the internal agenda (Ni), logically makes sense in the empirical world (Te), and reinforces the speaker's Fi. As a result, the not so important Se pays the price and the speaker is oblivious to his surroundings absorbed in thought and publishing in conversation those points that are critical--probably not noticing or not caring to notice when the eyes go shut. Second, hand motion and touching physical objects while speaking is linked to a few things. Setting MBTI aside for a moment, I find that people who tend to this are typically more energetic, enthusiastic, and thus cannot possibly restrict all that they wish to communicate strictly to words. Further, not only would this be contrary to the nature of an energetic type but in addition an intelligent person knows the value of using other devices to enable more effective communication. In addition to verbal content, these devices include tone of voice, dynamics, tempo, accents, body language, facial expressions, and so forth. Thus, in addition to precision in dictum the intelligent INTJ will draw upon such devices (such as using hand movements in conjunction with certain words and touching things to bring the abstract down to the concrete) to help communicate his or her ideas. The counterpoint to be is, however, that under certain conditions these physical motions may distract or take away from, rather than enhance, that which is being communicated. Indeed, I have a friend who has a sort of ADD when he talks sometimes, and constantly feels compelled to touch random things and point to unrelated objects as he speaks. To someone who doesn't know him, it would be quite humorous. But in his own head this helps him make sense of the world and vent his energies in more ways than using plain English. As a result, his own perception of his communication may not square well with actual realities at times. Nevertheless, if one possesses good judgment, is measured, and understands people, they will be able to use this to their own utility and it can be quite adventageous so long as it enhances rather than distorts communication. Now, I mentioned briefly that intonation, dynamics, tempo, can be used in communication. Interestingly, these are all important elements in musicianship. My guess is that musicians, who have an intuitive capacity to fine-tune such devices, will on average have a high potential for effective speaking. For instance, Bill Clinton who is considered a highly charismatic speaker by many played the tenor saxophone. One is not necessarily the cause of the other, but the two often coincide. Thus, we can establish that developing a better ear and sense of musicianship, when accompanied with confidence, can lead to better speaking and, by extension, communication.
, but I'm really happy I stuck it out and read through your post. You make some very insightful observations. One of my favorite things is watching (usually quiet) INTJs hang on the fringe of a conversation silently, and suddenly bursting into some animated, brilliant insight, handing flying. 
It's fun, and worth waiting for.
