But you can't control the fact that you know it's a lie, and that's likely what this method will be able to detect.

As you as you can be at hiding the fact that you're lying, the fact that you know you're not telling the truth will be a disadvantage, if only at a neurological level.

When people recall an event, they will tend to look in a certain direction. 90% of males and 60% of females will look to the left. When inventing or creating an image of recall, they will look in another direction. Almost all people will look up and to the left, or up and to the right. To determine if someone is recalling an actual event or inventing it, a baseline of eye movement should be established. To establish their baseline, ask a person a question that they will need to recall the answer. Example, "Do you remember what you had for dinner last night?" Watch their eyes. Sometime later, ask the same person a question that will cause them to create a response. An example might be, "If an elephant and a zebra had a baby, what do you suppose that baby would look like?" Again, watch their eyes. The eye movement may last only a fraction of a second, but it is telling nonetheless. You now have an eye movement baseline for that person.

Sometime later, ask that same person an open ended question and watch their eyes. "What did you do last night?" Another surefire way to detect deception is if the they stare straight back at you and become defensive. If they do this, they are hiding something and merely trying to turn the tables as a method of distraction. Again, this is a very basic portion of total interrogatory technique. Other clues that may come into play include body positioning, posturing, method of denial, or distraction.

"Accessing cues" happen when a person retrieves information that isn't easily accessible from consciousness. If someone has been practicing or rehearsing a lie, they won't necessarily require a noticable accessing cue to get it.
A 'constructed' cue might still happen when they're remembering. The circa-1977 NLP eye accessing model says rightward eye movements accompany Visual or Auditory CONSTRUCTED information. But people construct images/sounds for all kinds of reasons. Bandler and Grinder explicitly say in Frogs Into Princes that many people reconstruct their memories, and show a 'construct' eye accessing cue even when remembering. In fact, on a biochemical level, all memories are 'constructed'1 How 'constructed' a memory has to be to trigger that eye accessing pattern isn't clear. Of course, people don't necessarily access the information you think they're accessing. I did my undergraduate MIT thesis on validating the eye accessing cue model 2. My experimental protocol found no correlation, though my own personal impression of the model's validity was reinforced during debriefing. As part of the experiment, I asked, "How many chairs do you have in your living room?" expecting them to access visual information. They would have a KINESTHETIC eye accessing cue. That counted as a non-correlation. During the debrief, the subject said, "Remember when you asked about the chairs? I suddenly remembered how wonderful it felt when my mother rocked me to sleep in those chairs." (He went on about the wonderful FEELING for a few more seconds.) Just because I wanted him to access certain information didn't mean he did.
In police interrogation, I can imagine anyone--innocent or not--worrying about how their answers will be taken. If they worry by constructing scenarios in their mind, that could produce a 'constructed' accessing cue.
Finally, there are other models of eye movement which are taught in more recent NLP seminars that have little to do with the original accessing cues. Accessing memories is only the first step in using the information. Once accessed, a person arranges the information spacially around them according to their "submodalities" and for associated pictures/sounds, according to the content of the information. At this point, a righthand glance might be an accessing cue or might be a reference to information spacially located to the right.
A better approach to lie detection is to learn to notice unconscious physiological responses: pupil dilation, pore size, skin flush, muscle tone changes, breathing, etc. Calibrate carefully. Ask lots of questions that you know the answers to, until you are sure you can tell what combinations of nonverbal responses correspond to truth. If they happen to lie to one of your questions and you know they're lying, you'll also have the chance to calibrate a lie. Good poker players do this when they look for a "tell" in the other players.
Then when you interrogate, watch for deviations in their nonverbal behavior. Those won't necessarily mean they're lying, but they will point to areas where the person--for whatever reason--had a significantly different internal response.
You want to calibrate with questions as close as possible to the intensity of the questions you'll be asking. If you calibrate 'truth' by asking, "Were you born on January 3, 1970?" and then interrogate with, "Did you fire two shotgun blasts into the gas station attendant at point blank range?" you'll likely get different nonverbals simply because of the relative intensity of the two questions.
I've heard that voice tone often changes when someone is lying. Since voice tone is pretty unconscious in the Western world, it's often outside the awareness of the liar. So calibrating on voice tone might be another fruitful tack to take.
But so far as I know, there's no absolute way to know if someone's lying. Human beings are far too complex for our current understanding to give definite results.