Virgo girl with a crush on a gemini guy

I like this guy in my class a lot.
I think he's funny, charming, and really intelligent (boy oh boy can he lead a discussion about Baudelaire)
Anyways, I've noticed that in class when I'm looking at the teacher I notice him looking at me in my peripheral vision
and when I turn to see who it is, it's him and also when he realizes that I've 'caught' him staring at me he hurriedly looks away with a slight sense of embarrassment. And I know that I'm not just imagining it because my friend who's also in the class tells me that she sees him looking at me also.

SO, my question is for all you gemini's (especially gemini guys) should I make the first move by going and sitting next to him during class or would that drive him away since they tend to like 'the chase'?

p.s.
I'd also like to mention that he was born on the cusp between gemini and cancer but still technically a gemini.
and his rising sign is Virgo

Maybe find a way to exchange phone numbers and start texting/calling each other?