When writing.... actions define your characters
How do I make a character, who’s kind of reclusive, show his emotions? Writing really is the study of human beings and how they express themselves. Every opportunity you can, really observe (like you’re a being from another world) how the humans that surround you express the vast array of emotions that color our daily lives.
You’re right, some people are emotionally withheld the merest lift of an eyebrow says volumes about what's going on in their heads. Other people are like fireworks displays about everything - love, hate, happiness, boredom it all gets colored with some incredible display of emotion. The films that affect us the most are the films where the writer has created a visual language that relays even the tiniest detail of a characters inner landscape (emotional landscape) to us, the audience.
So, give some thought to the multitude of non-verbal bits of communication that are peppered throughout your day. Your child opens it's arms wide for a hug when you come home, but doesn't say anything. Your boss merely crooks a finger in your direction and disappears into her office. You know you've been summoned. At a chai shop, a handsome fellow merely meets your eyes over the lip of his cup, which mostly hides his smile of acknowledgement. You tell me what that means!!
Start cataloging in your mind the various ways people show us every day what they're thinking - instead of using words. Do this for a month and you will be on your way to understanding one of the key elements of screenwriting. Show - don't TELL what the characters are thinking.
I hope this helps. And I do wish you good luck with your writing.