Okay here's some tips for you after reading your post, and some general eye contact advice too. I have good eye contact skills. In fact I'd say it's probably what generates the most initial attraction in my case, eye contact is VERY seductive and powerful. My advice is don't try and dissipate the tension with a smile etc. Just enjoy the sexual tension. Remember she's staring you down too so if she holds eye contact she's being just as "creepy", and if she holds it for a bit too long she probably feels that sexual tension and attraction. Having a sexy girl staring into your eyes feels good. So just take a moment to enjoy that feeling, notice the intensity of the emotions it invokes. Don't instantly smile. Back in high school there was one time in class where this model girl (legit model, weirdly I saw a picture of her in a catalog earlier today, hadn't seen her in years) just locked eyes with me and we literally just stared into each other's eyes for upwards of 10 minutes. Yes, THAT long, zero smiling just "feeling it". It wasn't creepy, it just turned me on. She actually approached me later with her friend and pretty much the whole year consisted of her hooking up with me. A lot of times in the middle of classes she'd bend over in front of me, give me sexual looks, feel each other up under the desk, all sorts of hotness... I tell you what I looked forward to lessons where she was in my class... Anyway I've gone a bit off topic you don't need to know about the boring details of my personal life. So I'll try and summarize:
When you make eye contact with a girl, don't just see it as a method of picking her up, just allow yourself to FEEL that intensity. This means remaining centred in yourself and your emotions... Not wandering off in your head thinking "this is awkward she probably finds this creepy? Have I stared for too long? Should I do this? Should I do that?" No. Just FEEL how ****ing outright SEXY it feels when a HOT girl is staring deep into your eyes. If your mind is in the right place and way of thinking, you will be able to experience those emotions. If you're too worried about what SHE'S thinking it will be awkward and probably creep her out/ have no emotional effect on her.
I imagine what you're doing is staring in their eyes for 0.1 seconds and smiling. As an example of what I mean, you know how in romance films when the two to-be lovers first see each other? See how they're looking at each other feeling that emotion, like "woah" rather than instantly smiling like a dork... And notice how there's emotion in it not just a blank stare because he thinks it's "what he should be doing"...
Be careful though you don't want to come across Bundy-like (CAUTION: Once she's looked away DON'T STAY FIXATED ON HER EYES. If she turns her head, then turns back and you're still deadpanning into her eyes and haven't moved a muscle that's CREEPY, picture it in your head to see what I mean), you should feel what she's feeling by the way she looks back at you. Again don't try to think about it, it will come across in almost a psychic way whether she's "feeling it" or not, if she IS, keep going, this means you're BOTH interested, she knows you are and you should realize so is she. You'll know if she's turned on/feeling the tension or if she's finding it weird. I've actually never met another guy in my whole life who does this and they're missing out. They always either smile too quickly and don't feel the sexuality or they look away really quickly without feeling it. You can smile at some points... For example if you're standing and a cute girl walks past locking eyes with you, maybe shoot her a smile at the point where she's walked past and taken a couple more steps with her head turned back to you... Things like that... Actually forget that example just enjoy the sexuality of it and do whatever feels right, you WILL know. I do this VERY often and the reactions you get are INSANE. I have never been called "creepy" or received a weirded out look because of it. Okay once I misjudged a girl's reaction and thought it was ON, and she turned to her friend like "why is this guy looking at me?" But believe me that was one time out of THOUSANDS and due to my own misjudgment. Oh and one final important thing, don't make weird "sexy" face expressions, you don't even need to, and it might come across in a weird way if you're forcing them on, or maybe desparate if you're squinting like you haven't had sex in years. It's all about calibration. There are inappropriate moments e.g. standing next to her whilst she's shopping, I can't say much more it's already tl;dr just use some social intelligence too.
