You've characterized what the act of honing emotional intuition needs, then what one would actually look like: block distractions, go for a long walk, generally think about the things you're uncomfortable about but let your mind wander. I think the hard part is, how much time do you need to devote before you get something back out of it? Best policy is probably just "always do it."

And in the last line, you elicited a reaction from me to say "This isn't hippy bs" and buy in to what you've said. Thanks for the deceptively good answer :D