Eye contact is one of the most important non-verbal channels of communication that we have. Eye contact gives the unconscious signal that trust is in the air. When you avoid looking a judge directly in the eyes, you are signaling a lack of confidence and really, that you do not want that crown.
In interview, your message will go where your voice goes and your voice will go where your eyes send it. If you are sending a message to the ceiling, look at the ceiling. If you are sending a message to the judge's eyebrows, then talk to the eyebrows. But I believe (and correct me if I am wrong) that when you are in an interview (pageant or job), that you are sending your message directly to someone - the judge or the interviewer. Stop wasting time look all over the place and send your message straight to the eyes. I'm not telling you to be creepy and stare them down - naturally, we as humans look away for a second to process something, but look the judge in the eye when answering. Not doing so could signal lying or lack of confidence.
The same rule applies on stage. If you want the judge to "pick you", you need to send that message to the judge. Why some girls look at the back of the ballroom or above a judge's head is beyond me - is the back of the ballroom or a bald spot scoring you? You must look the judge in the eye to be taken seriously. Again, no scary stares, please, but send me the message that you are confident in what you are doing on that stage. And for heavens sake, don't 'turn it on' when you are directly in front of the judges; use that walk on time wisely too.
You can always add a smile in that interview room or on stage too! A smile is the best way to put your best foot forward. Just like yawns or sneezes, smiles can be contagious too. While a judge is asking a question or you are preparing on walk on stage, smile. Break the barrier. While on stage, always smile. Avoid creepiness, as always, but smile to say "I'm approachable," "I'm happy to be here", and "I'm confident".
Combine that smile and direct eye contact and you can definitely improve your score. Radiate and give off the idea that you are confident, happy, and approachable; that's never failed anyone.