In this study, we adapted a race-Implicit Association Test (race-IAT) to mouse-tracking (MT) technique to identify the more representative target observed MT-metrics and explore the temporal unfolding of the cognitive conflict emerging during the categorisation task. Participants of Western European descent performed a standard keyboard-response race-IAT (RT-race-IAT) and an MT-race-IAT with the same structure. From a behavioural point of view, our sample showed a typical Congruency Effect, thus a pro-White implicit bias, in the RT-race-IAT. In addition, in the MT-race-IAT, the MT-metrics showed a similar Congruency Effect mirroring the higher attraction of the averaged-trajectories towards the incorrect response button in incongruent than congruent trials. Moreover, these MT-metrics were positively associated with RT-race-IAT scores, strengthening the MT approach's validity in characterising the implicit bias. Furthermore, the distributional analyses showed that mouse trajectories displayed a smooth profile both in congruent and incongruent trials to indicate that the unfolding of the decision process and the raised conflict is guided by dynamical cognitive processing. This latter continuous competition process was studied using a novel phase-based approach which allowed to temporally dissect an Early, a Mid and a Late phase, each of which may differently reflect the decision conflict between automatic and controlled responses in the evolution of the mouse movement towards the target response. Our results show that the MT approach provides an accurate and finer-grained characterisation of the implicit racial attitude than classical RT-IAT. Finally, our novel phase-based approach can be an effective tool to shed light on the implicit conflict processing emerging in a categorisation task with a promising transferable value in different cognitive and neuropsychological fields.