What does being hungry look and sound like when it comes to being interviewed?

Maybe expressing high enthusiasm during an interview is not in your personality. 

Should that automatically rule you out?

Internally, you are indeed excited about this opportunity.

You just don’t feel the need to go in with pom poms, and a megaphone, cheering “rah, rah”.

Are there other ways that you can express heightened interest? 

Often hiring managers are looking for something to help you stand out from the others.

This might be considered “hunger”.

Maybe for you, subtle words is all that’s needed.