Variation in human gaze can be explained by a variety of factors. Within an individual, gaze patterns can be quite reliable and can be explained in part by heritable common genetic mechanisms. If individual gaze patterns are strongly idiosyncratic, could they enable highly accurate detection of individuals via a 'gaze fingerprint'? And are gaze fingerprints linked to variation in phenotypes such as autistic traits, which are underpinned by heritable common genetic mechanisms and cause atypical and idiosyncratic gaze to manifest in early development? To answer these questions we utilized a stimulus-rich design where participants viewed 700 stimuli of complex natural scenes, repeated in two sessions separated by ~1-2 weeks. Across independent discovery (n=105) and replication (n=46) datasets, we find that gaze fingerprinting occurs at high rates (50-65%) relative to chance (1-2%) when gaze similarity is averaged across stimuli. However, such averaging procedures hide a unique non- random individuating code represented as a multivariate 'gaze fingerprint barcode' pattern across all 700 stimuli. Within such barcodes, around 94-95% of all individuals had fingerprintable stimuli counts that were significantly higher than situations where identity is randomly permuted. Data-driven clustering of such barcodes results in each individual as its own unique cluster. A small subtype of individuals can be replicably identified, whose fingerprintable stimuli are highly enriched for human, social, face, and emotion features. Finally, increased 'gaze fingerprintability' is associated with decreased levels of autistic traits. Overall, this work showcases that gaze fingerprints are important precision biomarkers and may have translational relevance to conditions like autism.