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A novel eye-tracked measure of the frequency of pupil diameter oscillation is proposed for capturing what is thought to be an indicator of cognitive load. The proposed metric, termed the Index of Pupillary Activity, is shown to discriminate task difficulty vis-a-vis cognitive load (if the implied causality can be assumed) in an experiment where participants performed easy and difficult mental arithmetic tasks while fixating a central target (a requirement for replication of prior work). The paper's contribution is twofold: full documentation is provided for the calculation of the proposed measurement which can be considered as an alternative to the existing proprietary Index of Cognitive Activity (ICA). Thus, it is possible for researchers to replicate the experiment and build their own software which implements this measurement. Second, several aspects of the ICA are approached in a more data-sensitive way with the goal of improving the measurement's performance.