Do reserved guys take time to open up to a girl they like?

This male coworker and I are in talking stage. He never shares anything about his personal life at work while few of us others will share what we did for weekend and about other personal stuff. He has only one social media profile which is set to private.

I have noticed that he dodges very general personal questions I ask him when we are both texting. Otherwise, he replies within seconds, tells me his likes/dislikes and keeps the chat going from his side. I find this odd considering he likes me but at the same time, I think that probably he is one of those reserved guys who opens up to only those few people that he trusts. We both are starting to know each other.

Do reserved guys take time to open up to a girl they like?
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