This paper investigates the application of novel eye-tracking metrics to assess cognitive load in visual decision-making processes. In particular, it aims to contribute to understanding the cognitive process and developing complementary measures for evaluating visual behavior in neonatal pain assessment. We have carried out an eye-tracking study using the relative Explore-Exploit Ratio proposed and the application of the Task-Evoked Pupillary Response to evaluate pediatrician experts, non-experts, and parents while analyzing frontal facial faces of distinct newborns, before and after painful procedures, from a benchmark dataset considering areas of interest clinically relevant. The Tobii TX300 eye-tracking system recorded this data in a closed room with controlled lighting. Our results disclose that the visual attention described by the traditional metrics may not correspond directly to the respective fixation patterns and pupillary changes quantified for all the sample groups of participants investigated, highlighting statistically significant differences in the visual behavior between experts and non-experts in such vital decision-making tasks