So I'm still pretty shitty at this stuff, but I figured "hey, I have eye contact down - no need to worry about that."

WRONG. There is a difference in eye contact. There's making eye contact, and then there's peering into your soul eye contact. You want to be doing the second one. You shouldn't be simply making eye contact, you should be focusing so intensely on their pupils that you can really only focus on one eye at a time, the rest of their face should be outside your focused sight entirely.

Now, don't get crazy or try and do this too much, because it'll just be creepy. However, when they are talking to you, I've found it remarkably helpful to use this sort of intense and intimate eye contact with one-on-one conversations.

To give an example from my life, I was fortunate enough to meet Derek Sivers at a music conference a few years ago, and he sort of took me under his wing for the day. He's a brilliant guy, but what impressed me the most was his ability to make everyone at the table feel like he cared. He definitely gave me the most intense eye contact I had experienced to that date, and I won't lie...I felt fucking special. I felt so heard, and it never seemed like he was listening to be polite or waiting to talk, he was utterly, completely engaged in what I was saying. This was almost entirely accomplished with eye contact. It was enormously flattering, and I actually felt better about myself because he seemed so genuinely interested in what I had to say.

So yeah, when you make eye contact it should be like I fucking dare you to break this gaze, there is nothing else in the world that matters to me more right now than this conversation, and I am so focused on you that a homeless person could be murdered two feet away from me and I wouldn't even fucking notice. And then actually do it. If you're busy thinking:

Oh fuck what do I say, damn nice boobs, she's hot, she's too hot to actually be interested in talking to me, ugh is she looking at my shirt? I knew I shouldn't have worn this shirt. Oh fuck she's done talking WHAT CAN I SAY THAT'S WITTY???

You are going to miss out on the whole thing. Live in the moment of the conversation, listen and engage in what they are actually saying and what they are trying to communicate with what they're saying, and then respond naturally.