We're talking about genuineness here as a connection, yeah? When we sense genuineness, somebody has touched us in a hard to describe, but particularly powerful way.
I was recently convinced that genuineness - authenticity, if you will - is rooted in vulnerability.
Genuineness is what we perceive when somebody allows their True Self to be vulnerable. It is the TS that we spend our life protecting with our enneagram type behaviors. It is very much correlated to type, as each type protects themselves from different things in different ways. Every time there is a threat to the TS, we throw up some kind of shield, something that masks the genuine part of us in an effort to shield us from pain - be it withdrawal, denial, apathy, projection, and so on.
The authentic person is the one who learns to leave the shields down, even when they are under threat. They touch us because we're constantly comparing ourselves to everybody else, and when we see somebody who has few or no shields protecting their fragile, unique selves we are either inspired (projecting lost qualities upon them that we wish we could recapture in ourselves) or threatened (our own shields go up because something in our perceptions make us feel vulnerable).
The gurus of the enneagram have figured all this out already, but don't articulate it very clearly. The psychological health spectrum and growth suggestions described by Riso and Hudson (among others) are a road map to authenticity: To become authentic, you need to lower the shields. To lower the shields, you need to know what they are, which means knowing your type. You then need to make the type-specific changes to your life. As you grow, your behaviors will naturally start to coincide with higher levels of the psychological health spectrum.
Ultimately, the most genuine people are the ones who are in the healthy categories of their type. Their genuineness recognizable, but how one reacts to it depends on their own type and psychological health.
I mentioned that I was recently convinced. The connection for me was made while I was studying the work of a scholar named Brene Brown. Check out her TED talks on youtube.