Recognising these traits, and benefits and limitations that each can lead to, is definitely an important piece in the puzzle of understanding character.
The study of Archetypes however pays no consideration to the dimensions of introvertedness or extrovertedness as these traits are not tied to any particular archetype but can be applied to any one of them.
There may be a tendency for the deep thinking Sage to be more introvert in their nature, and the more passionate Warriors and Lovers to be, on the whole, more expressive and thus extrovert. Yet we need to be careful not to generalise and make this true for all cases. We should not immediately make assumptions but assess the matter separately.
I would always use the most simple test to help a coaching client get clear on the matter.
The one question to ask, that immediately reveals whether someone is more introverted or extroverted in their nature, is to ask what they do to recharge.
What do you do to recharge?
Party or solitude? Do you get together with other people or do you seek out time alone.
The extroverts always seek out a group of people with whom they get on as this recharges their batteries the fastest - it's as if they need a stimulating environment where the interplay with other people generates new energy and revitalises them from the outside in.
Introverts need the exact opposite. They need time and space to be alone because they recharge from the inside out and if there's too much stimulation going on around them they simply can't connect to the inspiration or energy they need from the inside.
This is an important distinction and is one that every corporate manager needs to be aware of as they assess the schedules that they expect the individuals on their team to follow.
It also helps individuals and families to plan their days including holidays in such a way that they each create the environment they need to recharge.
So there are no strictly introverted or extroverted archetypes in this universal archetype model that we use in Team Me. Instead it is important that we assess the matter separately and include our conclusions in a more holistic assessment of the individuals concerned.
Types, including Archetypes, form one dimension of human expression but clearly do not amount to the whole story. Other dimensions, such as gender, introvertedness/extravertedness and more besides are also really important.
So let's continue to create an integrated understanding of ourselves and the others around us from a multitude of perspectives so that we create the fullest picture possible where nothing is ignored and nothing is missing.