I can give you my own informal study in observing the driving needs in the standard temperament matrix:
Temperament for Dummies
(Keep in mind, that I'm using the five temperament system, where the interaction styles are known by the original Galen "humor" names, "Informative" is known as "responsive" or "relationship oriented", and "directive" is known as "task-oriented", and the new temperament Supine is Introverted/Responsive, while Phlegmatic is now moderate in both scales. For the sake of comparison, you can just merge those two temperaments back together; both fitting the ISF/INP interaction style. Also, Melancholy=IST/INJ, Choleric=EST/ENJ and Sanguine=ESF/ENP. The Keirseyan temperament groupings SJ/SP/NF/NT also loosely correspond, with cooperative/pragmatic as expressiveness, and structure/motive as responsiveness, so those can be factored in people's self or others image as well).
Introversion itself seems to be energized by fear of rejection (or criticism and feelings of inadequacy), which is a common feature of the introverted temperaments [in the APS descriptions]. How a this leads a person to respond to people (wanting or not wanting to be approached by others) is determined by the driving need of the task/relationship scale.
Extroversion seems to be energized by a need for attention (or recognition of adequacy). What the person does with this as he approaches people (relate to or use them) again depends on task/relationship.
Relationship-oriented behavior is energized by the need for acceptance (or recognition of worth). How they try to gain this acceptance (make the first move towards others or wish others would make the first move) is determined by E/I.
Task-oriented behavior is energized by distrust of others (the way others do things, etc). What the person does with this distrust (fear or dominate others) is determined by E/I.
So fear of rejection plus distrust of others equals the introverted-task oriented rejection of others first and fear of the unknown. (Melancholy)
The fear of rejection plus the need for acceptance equals the introverted-relationship oriented shyness, and desire to serve others. (Supine)
The need of attention plus the need of acceptance causes one to be extroverted and relationship oriented, and accept and charm everyone and be the life of the party (and still maintain a fear of rejection, but unlike the introverts, this is not the primary drive). (Sanguine)
The need for attention plus the distrust of others causes one to be extroverted and task oriented, and be outgoing to only use others for his own achievements. (Choleric)
So "self-image", and "others-image" are also involved. Introverts, from the descriptions, tend to have low self-esteem. They doubt their worth, either as a person (Inclusion/Affection), or in their capabilities or adequacy (Control). Hence, they are afraid to express, fearing their inadequacy will be revealed. Extroverts tend to have a higher self-image. They have the confidence to charm or use people (I/A), or lead and control them (C), so they freely express to them with no problem. They believe they have the adequacy; they just want others to recognize it.
Task-oriented people will have a lower image of others. They do not trust them, or value them; either who they are (I/A), or what they do (C). So they will not want interaction from others. Relationship-oriented people will value others, and hence want them for who they are, and to gain acceptance from them for their own worth (I/A), or will depend on them in some way in what they do (C).
Hence, the Melancholy tends not to like himself OR others, and thus rejects others figuring they reject him anyway; and likes solitude to immerse himself in his own world of thinking and tasks, or at least his own sphere of control (family, etc). The Choleric does like himself, and people are not liked as people, but as "objects", as APS describes it. So he will only deal with them according to his own terms. The Sanguine likes himself and likes others, and hence is very involved with people for both their own and his own sake. Liking who people are does give him a bit of vulnerability that the Choleric does not have, so the Sanguine has a fear of rejection similar to the introverts. His self esteem can crash if rejected. However, he will have more of a confidence to keep trying to win others acceptance and recognition. So he will bounce or "swing" back to his expressive, confident self rather quickly. The Supine is described as seeing worth in everyone else, but not himself. So he tries to serve others to gain acceptance. He has doubly the fear of others, being both introverted (fear of exposed inadequacy and hence, rejection or criticism), and needing people's acceptance (which makes one vulnerable to them) on top of it! The Phlegmatics, again, can just take people or leave them.
The familiar concept of "I'M OK; YOU'RE OK" (the expression being the example of the most "healthy" attitude) can thus be paired with the five temperaments:
Sanguine: "I'm OK; You're OK"
Melancholy: "I'm NOT OK; You're NOT OK"
Choleric: "I'm OK; You're NOT OK"
Supine: You're OK; I'm NOT OK
Phlegmatic: "I'm whatever; you're whatever"
All of this would make fear, vs. need of attention, and distrust vs. need of acceptance the "root of personality". These often are described as the basis of much of human behavior. So it would make sense that they would be the real root of temperament. These could be further summed up as "[Self]-Confidence" and "[others] reliance". The person with self confidence will believe in his worth and express to others to gain recognition of it. The person with less self-confidence will fear failure and rejection of some sort, and thus express less. The person who relies on others will stake his worth on others in some way. The person who does not rely on others will be independent, and basically see others as intruding on their space.