Real-time implementation of gaze-based \(2^{\textrm{nd}}\) -order metrics is given, including computation of the \(\mathcal {K}\) coefficient and gaze transition entropy. Innovations include strategies for real-time update of both metrics, dependent on instantaneous real-time binary gaze classification (saccades or fixations), normalization of the \(\mathcal {K}\) coefficient, and correction of gaze transition entropy so that special cases are better handled, including gaze fixating a specific Areas Of Interest (AOIs) for a prolonged period, or gaze falling outside of all defined AOIs. The resulting implementations are sensitive to the length of the history buffer maintained for either computation, but both produce intuitively interpretable estimates of gaze behavior. Both metrics are implemented in a context-free manner allowing for future use in eye-tracking systems that do not possess scene cameras and where there is a need for instantaneous gaze-based biometric measures, e.g., captured over the course of a day.