This paper compares the pupillary activity index to traditional eye-tracking metrics like the fixation count and duration in assessing neonatal pain. It explores the benefits of incorporating pupillary activity measures to improve methods that lead to an understanding of cognitive processing and performance evaluation. The estimation of cognitive load using pupil diameter typically involves measures relative to a baseline. Instead, we conducted an eye-tracking study using the Low/High Index of Pupillary Activity to evaluate healthcare experts and non-experts analyzing the faces with and without pain from a dataset of newborn faces. This data was recorded by the Tobii TX300 eye-tracking system in a closed room with controlled lighting. Our contribution is to introduce the LHIPA calculation considering the areas of interest segments of the pupil diameter signal. The results suggest that the visual attention reflected by the traditional metrics may not correspond directly to the respective cognitive load for both sample groups of participants.