In this study, we demonstrate the effects of anxiety and cognitive load on eye movement planning in an instrument flight task adhering to a single-sensor-single-indicator data visualisation design philosophy. The task was performed in neutral and anxiety conditions, while a low or high cognitive load, auditory n-back task was also performed. Cognitive load led to a reduction in the number of transitions between instruments, and impaired task performance. Changes in self-reported anxiety between the neutral and anxiety conditions positively correlated with changes in the randomness of eye movements between instruments, but only when cognitive load was high. Taken together, the results suggest that both cognitive load and anxiety impact gaze behavior, and that these effects should be explored when designing data visualization displays.