Irrespective of the precision, the inaccuracy of a pupil-based eye tracker is about 0.5 \(^\circ \) . This paper delves into two factors that potentially increase the inaccuracy of the gaze signal, namely, 1) Pupil-size changes and the pupil-size artefact (PSA) and 2) the putative inability of experienced individuals to precisely refixate a visual target. Experiment 1 utilizes a traditional pupil-CR eye tracker, while Experiment 2 employs a retinal eye tracker, the FreezeEye tracker, eliminating the pupil-based estimation. Results reveal that the PSA significantly affects gaze accuracy, introducing up to 0.5 \(^\circ \) inaccuracies during calibration and validation. Corrections based on the relation between pupil size and apparent gaze shift substantially reduce inaccuracies, underscoring the PSA’s influence on eye-tracking quality. Conversely, Experiment 2 demonstrates humans’ precise refixation abilities, suggesting that the accuracy of the gaze signal is not limited by human refixation inconsistencies.