As far as the eyes being the window to the soul, the Halacha is that on Shabbos we consider anything in the eyes to be a Sakana because, as the Gemara says, the eyes are rooted in the heart. Also, the Pasuk says, Ha’adam Yira’a La’einayim Viha’elokim Yir’a Laleivav. So I guess that’s as good a view we get.
On a plain level, you can see someone’s alertness in their eyes. Kindness is also visible in the eyes. The Gemara says that a cow has different eyes once it carried a yoke. I guess that’s where “Jewish eyes” come from.