Autism Spectrum Disorder (ASD) affects children's social and communication abilities, with eye-tracking widely used to identify atypical gaze patterns. While unsupervised clustering can automate the creation of areas of interest for gaze feature extraction, the use of internal cluster validity indices, like Silhouette Coefficient, to distinguish gaze pattern differences between ASD and typically developing (TD) children remains underexplored. We explore whether internal cluster validity indices can distinguish ASD from TD children. Specifically, we apply seven clustering algorithms to gaze points and extract 63 internal cluster validity indices to reveal correlations with ASD diagnosis. Using these indices, we train predictive models for ASD diagnosis. Experiments on three datasets demonstrate high predictive accuracy (81\% AUC), validating the effectiveness of these indices.