One of the things that makes it difficult for me is that I'm already connected to the character and I don't want them to hurt anymore. I try to protect them, shield them from the exposure writing their story will cause. It sounds silly when I say it because the reason I'm writing is to tell their story.
To overcome this, I often write scenes in first person before I then convert them to third person. You'd think if I'm writing as the person that I'd delve into the emotions, but it doesn't always work, particularly with those characters who aren't even aware they have emotions. They're so suppressed, they just get on with the action and expect everything else to work out afterwards.
My crit partners always say "They might not recognise they have emotions, but they will have them and there will be some sign of them: find that sign." Yeah, yeah, yeah: stop fluffing around the edges and go deep, dive into them, become them, feel everything they feel, then show you what that looks like from the outside.
I know the theory. I know how it's supposed to work and I want to achieve that connection, but sometimes I have trouble dealing with the emotion in my own life; diving into the emotion of someone else's is HARD.
Another method I use to work out how suppressed emotion is exhibited is to walk around the house... gesturing. Anger is one of the few socially acceptable forms of emotive expression. It's okay to get angry and it's okay to express it. But what if the character suppresses even that? What would his 'tells' be? What happens inside his body when he's angry and trying not to show it? How does that show on the outside to someone looking in?
Then I look at the gentler emotions. How does protectiveness appear when they can't express it? It might look a lot like anger: it's the socially accepted emotion, remember.
What about gentleness and caring? Those are more difficult. Often they come down to a softening of facial features, or aborted movements. Those are difficult to show from inside the character's head, though. Sometimes, they move, touch someone gently, without even realising it, but then you have the problem of autonomously moving body parts--that never ends well.
I'm thinking about all this today because the character I'm writing at the moment isn't even aware of a lot of his emotions. He doesn't use words like 'lonely' or 'protective' because he doesn't recognise what they are inside. He was sold into prostitution as an eight-year-old. He's always been lonely; he's never been protected. That's simply his state of being. It's normal for him, not unusual--certainly not recognised. So far, the only thing I've come up with to show these emotions with him is to show the lack of them after he's had the opposite for a short time. He has attention and company, and protection for a few short weeks, then they're gone. His 'normal' was different, but now it's back the way it was and it's no good anymore.
I'd love to know what others do with characters like this.