Archetypes can and would go together with things like introversion and extroversion, from what I understand, archetypes would be formed based on what is beneficial for the individual, such as appearing scary in order to get something you want, and people would manifest in different archetypes based on their natural strengths and tendencies.
Ehh, i would suggest you to ditch your current idea about archetypes completely and study the subject a bit more from some more reliable sources. For example people dont manifest in archetypes, but archetypes manifest in people. Archetypes are not formed by the person, but archetypes from the person etc etc, you got it all backwards :/
Archetypes are the structures of the collective unconscious, which is the inherited aspect of your psyche, which is shared by all people. All complexes(which are the structures of the personal unconscious) has roots in archetypes. So while we all share the same archetypal patterns in our fundamental brain wiring, those archetypes are personalized differently in different people. For example we all have the archetype of a hero, but how we relate to this inner hero and in what situations we act it out varies from person to person and is dependent on the persons complexes(and is not dependent on the persons type in any way).
Sure you can say that one person act out this hero often at one point of his life and is trying to catch people doing bad things. But when that guy gets stabbed and almost dies when trying to catch a graffiti artist, how he related to this archetype of a hero might change drastically, now he might not act it out at all.
This theory assumes that how the person relates to archetypes is something static(or if it doesent, choosing a career based on something that changes from moment to moment at least to some degree would be extremely stupid) and this obviously is not true. Also not to mention that the whole idea of personality(which this theory is trying to fit archetypes into) by definition is that the personality is reasonably static over time, and again how archetypes manifest in people is not something static, hence they cant be used to type personality. I could go on and on about explaining this, but i dont really care to do that, so im just going to suggest that you read Jung or some good sources on Jungs ideas like the journal of analytical psychology or books of jungian therapists.