Eye tracking is a powerful technique that helps reveal how people process visual information. This paper discusses a novel metric for indicating expertise in visual information processing. Named the Gaze Relational Index (GRI), this metric is defined as the ratio of mean fixation duration to fixation count. Data from two eye-tracking studies of professional vision and visual expertise in using 3D dynamic medical visualizations are presented as cases to illustrate the suitability and additional benefits of the GRI. Calculated values of the GRI were higher for novices than for experts, and higher in non-representative, semi-familiar / unfamiliar task conditions than in domain-representative familiar tasks. These differences in GRI suggest that, compared to novices, experts engaged in more knowledge-driven, top-down processing that was characterized by quick, exploratory visual search. We discuss future research aiming to replicate the GRI in professional domains with complex visual stimuli and to identify the moderating role of cognitive ability on GRI estimates.