It reads to me as your not 100% sure what your boss means by being more engaged at work or what that might look like.

I work with IT and introverts are more the norm then exception so its confusing to me that a manager would not recognize this reality… and its benefits.  (ref  ‘Quiet: The Power of Introverts in a World That Can’t Stop Talking’  by Susan Cain)

Is there anything specific about your work that your boss wants you to improve or is it all inter-personal issues? As an observer looking in you need more specific instruction and goals to work towards.

At least one-third of the people we know are introverts. They are the ones who prefer listening to speaking; who innovate and create but dislike self-promotion; who favor working on their own over working in teams. It is to introverts—Rosa Parks, Chopin, Dr. Seuss, Steve Wozniak—that we owe many of the great contributions to society.

In Quiet, Susan Cain argues that we dramatically undervalue introverts and shows how much we lose in doing so. She charts the rise of the Extrovert Ideal throughout the twentieth century and explores how deeply it has come to permeate our culture. She also introduces us to successful introverts—from a witty, high-octane public speaker who recharges in solitude after his talks, to a record-breaking salesman who quietly taps into the power of questions. Passionately argued, superbly researched, and filled with indelible stories of real people, Quiet has the power to permanently change how we see introverts and, equally important, how they see themselves.

Ah yes, fake it till you make it. That can work in certain situations, however my feeling is that its best to be genuine. That said learning to be better at communication and engaged with others takes practice so going in with the perspective of let’s see what works could be a less stressful approach then needing to be perfect every time. (A curse of being an introvert is a tendency to need to be perfect and not to “embarrass” ourselves.) Your written communication is very strong as is your engagement in your post, so you have a lot to work with.

I always hated the ‘speak up more in meetings’ comment on my reviews. I have learned to speak up in a meeting when I have something to say but for the most part I play the role of active listener. Making eye contact every now and then with who ever is speaking, leaning towards them (not in a creepy way) and nodding and smiling when appropriate. In this way I remain engaged even when quite. Funny side affect, it has been pointed out to me that often in a meeting people will be “talking” to me.  To be candid I’m hard of hearing so I have to be a active listener but my managers don’t need to know that. ?

You have additional challenge if your dealing with customers. Again, being an active listener can help with engagement. This is not about faking it but being genuine… assuming you care about your customers, which I bet you do. Such interactions are a great place to practice compassion while maintaining one’s personal boundaries. As an introvert you likely have developed a natural empathy and its ok to let that show.