The "Reading the Mind in the Eyes Test" (RMET) is one of the most used tests of theory of mind. Its principle is to match an emotion word to the corresponding face image. The performance at this test has been associated with multiple psychological variables including personality, loneliness and empathy. Recently, however, the validity of the RMET has been questioned. An alternative version of the test has been tested using eye-tracking (Russell et al., 2021) in addition to manual responses and was hypothesized to be more sensitive. Here, we put this hypothesis to the test by attempting to reproduce already-assessed correlational results between the performance at the classical RMET and the self-reported personality, loneliness and empathy, now using eye-gaze as an RMET performance index. Despite a marked eye-gaze bias towards the face image corresponding to the target word, the eye-gaze pattern correlated with none of the self-reported psychological variables. This result highlights the interest in using eye-tracking for theory of mind tests, while questioning the robustness of the association between psychological variables and RMET performance, and the validity of the RMET itself.