What to do when students are not keeping their eyes on their own test?

There are a few reasonable approaches, and they vary mostly in (a) intrusiveness towards the students and (b) effectiveness

• Walk intently in the direction of the student, cough, and stare at them for a minute. From the perspective of the "potentially cheating student", this is quite effective. There's no way they'll pull any funny business while you're actively looking at them and no one else. And they now know you're aware of them, so they might be less likely to try something later when you're across the room but have them on your mind. However, this can call attention to you and the student you're watching, depending on how loud you make your ahemming and how intent you make your staring. Although, if the eye-wandering is particularly glaring, you might want to make your staring obvious and deterrent.
• Speak to the room at large, reminding them that they should keep their eyes on their own paper and cheating will be punished. The great thing about this is that you can do it whether you see one pair or twelve pairs of wandering eyes. You can say it not only while scanning your eyes across the room but also while the students see you scanning your eyes across the room, so they don't feel individually called out for crimes (falsely or otherwise) and they also feel like you're being vigilant. The bad thing about this is that it can disrupt focused students. If I were intently working on a problem and were all of a sudden snapped out of my concentration to be reminded not to cheat (which I wasn't doing anyway), I might be miffed.
• Call out a potential offender and either move them to a new seat or take away their test. This is quite disruptive, of course, but can be effective if you are sure of your accusations. I have subtly done this, by asking students to spread out amongst an otherwise unoccupied row and then hovering near them for the rest of the hour. This is certainly disruptive to them, but I presume they were already suffering the cognitive dissonance of academic dishonesty and my ascertainment of that won't adversely affect them. Of course, if I'm wrong, this can totally backfire. So it behooves one to be absolutely sure that cheating almost occurred (or did occur).

I have tried variants of these methods quite effectively, depending on the situation. The following idea has not been tested by me, but I believe it could be effectively implemented.

• Have a pre-determined method for handling "cheating accusations" in your syllabus, and make students sign it. For instance, include a paragraph in your syllabus that says something like, "If I see you doing something during an exam that constitutes academic dishonesty, I will jot it down and dock you 10 points on your score [or whatever penalty is appropriate, you feel]. You will learn of this when you receive your exam back; I will not call you out during the exam to avoid distracting you and others. If you wish to dispute the penalty, we can approach the appropriate channels [i.e. the 'Academic Integrity Panel' or the 'Student Conscience Board' or what have you]." As I said, I have not tried this, so I wonder about its efficacy and, especially, its transparency to students ("Is this a blanket statement for him to penalize me unwarranted?" "Can I dispute his claim without contrary evidence? Can he even make a claim without evidence of his own" etc.)