I've had people close to me ask me which of my sides is "real." That has always struck me as peculiar. They both are. I like people. I just don't NEED them. My father was a truly bimodal person-- he had both needs. I've not known too many people that had extreme needs in both directions like that, but they must exist because he was one.
This resonates. I would self-identify as an extrovert with strong solitary tendencies, which is essentially that bimodal personality you describe. On most Jungian personality tests, I consistently score as just slightly extrovert, which fits.
In person, I'm a bona fide show pony, leading group conversations, hobnobbing, and generally loving the company of likeminded others. I live interpersonally. My best ideas come from discussions with close friends and colleagues. This is my preferred way of operating but, like a big cat, I'm short on stamina and long on rest. I NEED an hour or two each day to be immersed in people, but at least a few hours to let my ideas percolate, to exercise in solitude, and to just be. An extended social lunch or dinner contrasted with an otherwise solitary day is my ideal.
