You'd probably have better luck glancing at an eye to eye level rather than staring. Its just a brief moment of eye contact. From what I've learned, its only best to maintain eye-to eye contact while engaged in a conversation. And you have to use voice inflection so as not to bore the other person and seem sincere. If you want to build rapport with the person quickly, you can mirror their body language, subtly, as well. This comes naturally to NTs, but not to us, so practice is required. A good way to start is by doing it with someone you know and trust, preferably an NT. Let them know you want to improve your social skill and that you want to role play with them. You can practice with small talk, body language, and eye contact. As an added benefit to you, ask them how well you did. Be prepared for their honesty. If you get a negative reply, ask for clarification as to what you could've done better. Its probably best to do this with several different people so that you can develop a general sense of what is acceptable amongst varying personality types.
Another thing to do is to put yourself in a social setting and observe, observe, observe! You'll get a feel of what types of behaviors are suitable for you to mimic according to your own personality type. If you observe a behavior that doesn't feel right to you, then put it out of your mind. Keep the ones that appeal to you. A great way to do this is to wear sunglasses so as not to attract any attention toward yourself, allowing you to observe unnoticed. Just make sure that your face isn't blatantly pointed in their direction... kind of like you're a spy. Thats how I learned at least. So try it. It may take time. I
t took me a year of actively talking to people before I got over the fear of speaking with complete strangers. It took even longer to get where I am now. But just to shine a light in your direction I'll tell you this, it is never hopeless.
Good luck!
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Have fun being you!