The study of eye movements, particularly saccades and fixations, are fundamental to understanding the mechanisms of human cognition and perception. Accurate classification of these movements requires sensing technologies capable of capturing rapid dynamics without distortion. Event cameras, also known as Dynamic Vision Sensors (DVS), provide asynchronous recordings of changes in light intensity, thereby eliminating motion blur inherent in conventional frame-based cameras and offering superior temporal resolution and data efficiency. In this study, we introduce a synthetic dataset generated with Blender to simulate saccades and fixations under controlled conditions. Leveraging Spiking Neural Networks (SNNs), we evaluate its robustness by training two architectures and finetuning on real event data. The proposed models achieve up to 0.83 accuracy and maintain consistent performance across varying temporal resolutions, demonstrating stability in eye movement classification. Moreover, the use of SNNs with synthetic event streams yields substantial computational efficiency gains over artificial neural network (ANN) counterparts, underscoring the utility of synthetic data augmentation in advancing event-based vision. All code and datasets associated with this work is available at https: //github.com/Ikhadija-5/SynSacc-Dataset.