Is John an introvert or an extrovert? I remember reading a couple of things that made me think he was an extrovert, but I don't know.
My friend, this has been on my mind all day.
SO, obligatory disclaimer. I've got a masters degree in psychology, and my specialty was behavioral medicine, not personality traits or positive psychology, but we're gonna geek out anyway!
I'm going to approach this from the more updated perspective that introversion and extroversion exist on a continuum. Some people are very introverted and some people are very extroverted, and a lot of people are somewhere in between (ambiverts).
The first question I'd ask is, Does John "recharge" by spending time alone, or does he recharge in social situations? I'd say that it depends on the situation. We've seen him get a lot of enjoyment out of larger gatherings (the electric eel party comes to mind, though that ended pretty badly). But we also see him thrive in smaller, more intimate settings (particularly with people he's close with, like Jamie or Minnie or Harry Quarry). He frequents a social club and enjoys being around the other people there. Mixed results here.
Extroverts tend to be more action-oriented (which John is), excellent communicators (this too), and quick to make decisions (also this).
Introverts enjoy one-on-one conversations (John does), are more sociable with people they know (which John appears to be), and are introspective (that's for sure our boy).
John doesn't really seem to thrive on being the center of attention, but he deals with it. A lot of his extroverted traits are also part of his job (either as a commander, diplomat, or that vague "duty" associated with being "from a good family").
He also has this deep desire to really be known, to have some people in his life who know his secrets and care about him anyway. Considering John's biggest secret--his sexuality--is a capital crime in his time, the number of people that could extend to is very, very small by necessity.
All of that to say... I think or dear Lord John is actually an ambivert. He has a lot of extroverted characteristics, but he also has a lot of introverted characteristics. There are days he loves spending time around other people (parties, at the Beefsteak, etc), but there's also days when he'd prefer to just exist with as few people perceiving him as possible.
I'm not an expert on this though. I'd love to see what other people think!