Identifying physiological and behavioral markers for mental health conditions is a longstanding challenge in psychiatry. Depression and suicidal ideation, in particular, lack objective biomarkers, with screening and diagnosis primarily relying on self-reports and clinical interviews. Here, we investigate eye tracking as a potential marker modality for screening purposes. Eye movements are directly modulated by neuronal networks and have been associated with attentional and mood-related patterns; however, their predictive value for depression and suicidality remains unclear. We recorded eye-tracking sequences from 126 young adults as they read and responded to affective sentences, and subsequently developed a deep learning framework to predict their clinical status. The proposed model included separate branches for trials of positive and negative sentiment, and used 2D time-series representations to account for both intra-trial and inter-trial variations. We were able to identify depression and suicidal ideation with an area under the receiver operating curve (AUC) of 0.793 (95% CI: 0.765-0.819) against healthy controls, and suicidality specifically with 0.826 AUC (95% CI: 0.797-0.852). The model also exhibited moderate, yet significant, accuracy in differentiating depressed from suicidal participants, with 0.609 AUC (95% CI 0.571-0.646). Discriminative patterns emerge more strongly when assessing the data relative to response generation than relative to the onset time of the final word of the sentences. The most pronounced effects were observed for negative-sentiment sentences, that are congruent to depressed and suicidal participants. Our findings highlight eye tracking as an objective tool for mental health assessment and underscore the modulatory impact of emotional stimuli on cognitive processes affecting oculomotor control.