The issue of extrovert/introvert is an ancient issue:
Cicero, On Moral Duties, cites examples of the power of creating great impressions amongst groups of people:

"14. But while there are two kinds of speech, to one of which conversation belongs, to the other public debate,2 there is no doubt that the latter is most conducive to
the acquisition of fame (for it is that which we dignify by the name of eloquence); yet it is hard to say to what a degree agreeableness and affability of conversation win
favor. There are extant letters of Philip to Alexander, of Antipater to Cassander, and of Antigonus to Philip, — all three, as we learn, men of the greatest practical wisdom,
— in which they advise their sons to allure the minds of the multitude in their favor by kindliness of address, and to charm the soldiers by accosting them in a genial way."

The entire resource is here:
http://oll.libertyfund.org/?option=com_staticxt&staticfi...

Vivtruvius, one of the greatest engineers of all time, explained the difference between great artists and great well-known artists in his book De Architectura, Book III.
It basically says without being a saleperson or being well-connected your work is of little value.

"1. ...Socrates the wisest of men...observed that it had been well if men's breasts were open, and, as it were, with windows in them, so that every one might be acquainted with their sentiments. Would to God they had been so formed. We might then not only find out the virtues and vices of persons with facility, but being also enabled to obtain ocular knowledge of the science they profess, we might judge of their skill with certainty; whereby those who are really clever and learned would be held in proper esteem. But as
nature has not formed us after this fashion, the talents of many men lie concealed within them, and this renders it so difficult to lay down an accurate theory of any art. However
an artist may promise to exert his talents, if he have not either plenty of money, or a good connexion from his situation in life; or if he be not gifted with a good address or considerable eloquence, his study and application will go but little way to persuade persons that he is a competent artist."

The best modern day summarization is "Showhorses are loved, Workhorses are abused"

Now, enough ancient references, there are surprisingly few books that deal with the introvert/extrovert issue. Please don't think eloquence is a skill that comes naturally. Clint Eastwood, Chris Rock, Emeril Lagasse and Johnny Carson have all been described as introverts. Below I have a few business leaders and some resources they used to become emotionally intelligent - a more accurate term for extroversion. Learning this is like learning anything else, you will be able to critique other
people once you learn.

1. Huey P. Long, governor of Louisiana - grew up selling goods door-to-door

2. Sam Wiley, earlier computer pioneer - IBM training program, Church of Science
examples: Wiley says never reveal ideas in their infancy due to extreme prejudice against new ideas
Book: "A Thousand Dollars and an Idea"

3. Marc Ecko, read Daniel Goleman's book "Working with Emotional Intelligence"
https://www.mercy.edu/faculty/Georgas/inbs640/files/WhatMake...

4. Warren Buffet - Attended Dale Carnegie's How to Win Friends and Influence People training programs

5. Youtube: "Keys to the VIP" Canadian Broadcasting Corporation's Game Show shows how to influence people
http://www.youtube.com/watch?v=xHyt1BscZdg&feature=relat...

A resource I have used lately is a Teachers Training program. I learned how to control a classroom through establishing expectations.

Maybe someone can compile a list of training, instructional, and leadership programs

Most Holloywood stars attend an interview class before they appear on TV. I learned this when a guest on the Jay Leno show said "Oh Mr.X helped you prepare for interviews, I went
to him too. He's great isn't he?"

Unfortunately, I do not think there has ever been a book written about influence and social intelligence. The Carnegie courses are expensive - your work might pay for it - and I do not know if the focus has changed to a more business-oriented format. Hopefully Ms. Susan Cain's book is helpful in this regard.