I’m somewhere between the IE and the II, as you define them (or, I’m both), with maybe some small EI tendencies as I’ve gotten more socially adept in my old age.
I’ve heard introverts described as people who need alone time to recharge their batteries, even though they may very well enjoy socializing and being around other people, while extroverts are those who are energized by being around other people. By that definition, I guess I’m an introvert.
I can be perfectly happy being alone (like your II), but I’d be miserable if I were alone all the frickin’ time. I spent too many years on the outside looking in, desperately wishing I could partake in all the fun and friendship and socializing and camaraderie and love and sex and relationships that everyone else seemed to be enjoying. Now that I’ve matured (a bit), my circumstances have changed, and I’ve gotten better at life and social skills and such, I do have that in my life, and am much the happier for it. I like people, I like being around people, I need human contact, but at heart I am fairly introverted.