So what's the deal? Are you supposed to be totally off book, or only partly memorized? Should you walk into the audition as if you are stepping on set, or just know it well enough to have an "idea" of the character, and be open to direction? What is the right amount of memorization?
Here's the bottom line: It's impossible to give a connected performance when the script is getting in the way. If you are looking down at the words, then you are robbing the audience of these wonderful moments between the lines that reveal so much about the character. As an actor, how can you be truly listening, if you are just wondering what your next line is? It creates tension in your performance, uncertainty, which gets in the way of the spontaneity, the element of surprise, the unwritten "life moments,' and prevents you from being confident, present, and compelling. And remember: someone else will be more memorized and more prepared than you, so why not give this your best shot? There's so much competition, so why not go in and impress the hell out of them?
Now I'm not saying don't ever look down at the script, because for a 12 page series regular scene with lots of technical jargon, that may be close to impossible. I say bring in the script, but don't look at it. Especially for co-star and guest star auditions. It shows them you know what you are doing, but if you go up on lines, you can quickly glance down and find your way back without panicking. If you go in without a script in your hand, it makes everybody nervous.
When 200 people are reading for a role and reading the SAME lines over and over, it becomes less about what the character is saying, and more about what they are NOT saying, and sometimes that is revealed through a moment where you are truly listening, hearing these words for the first time, and are able to deliver a surprising and unexpected performance. It's these tiny, improvised "life" moments (a smile, a look away, a laugh, a moment of vulnerability in the pause) that allow an actor's true personality to shine through, which really separates you from the pack. It creates life beyond the words. If you are only focused on the lines, then you are missing these amazing, spontaneous moments, and throwing away a golden opportunity to show different parts of the character. The more you look down at the words, the more you kill those moments, the more predictable and safe your audition is, and the less likely you are to book the job.
On-camera auditions are about connection, eye contact, active listening, and seeing the thoughts behind the eyes, the images, the point of view, and the feelings. Every time an actor looks down to get their line, their eyelids act like a wall, and close off the viewer (the casting director, producer, writer), and we are reminded "Oh, that's an actor auditioning." It keeps us from going deeper into your world.
I think for actors to give a strong audition, it has to feel like it's NOT an audition, but rather a conversation. You have to show them something they haven't seen before. That comes with knowing the script so well that you don't even need it. You can just sit there, dive into the character, believe the circumstances, truly listen, and let the scene unfold from moment to moment, acting on your impulses, and trusting your preparation.