Yes!! This is a great idea, and of central interest to our research. The fundamental reason that eye movements are critical is that we can only see well in the fovea of our retinas... which is about 0.1% of your visual field (about the size of your thumbnail at arms length). Everywhere else, you are legally blind. So our visual systems choose where we put our central gaze points very carefully, and your internal model of the world around you is built from your eyes only actually seeing just a few points in the world, then your brain builds a simulations that you call your conscious perception. So how it is that the brain targets eye movements is critically important to visual neuroscience.
Magicians, if you think about it, could be described as performers who control your eye movements. And they have an intuitive feeling for what draws your eye movements best. Visual neuroscience (and us, specifically) is also trying to solve this problem in parallel by doing exactly what you suggest. We currently have a paper in review in which we have looked at what people choose to look at in a scene, and how they utilize their oculomotor system to target those areas and to optimize acquisition of critical information at those "interesting" (and salient) points of the scene. This study will be coming out of Susana's lab once published so keep your eyes peeled on her website for its release: http://smc.neuralcorrelate.comm