To address the limitations of traditional algorithms in detecting eye movement events, particularly in Parkinson''s disease (PD) patients, this study introduces Skip-AttSeqNet. It presents an innovative approach combining skip-connected, one-dimensional convolutional neural networks with an attention-enhanced, bidirectional long short-term memory network. This hybrid architecture significantly advances smooth pursuit (SP) event detection, as evidenced by its performance on both the GazeCom dataset and a unique dataset of PD patient eye movements. Key innovations in this work include the utilization of skip connections and attention mechanisms, along with optimized training-validation set division, collectively enhancing the model''s accuracy while mitigating overfitting. Skip-AttSeqNet outperforms existing algorithms, achieving a 3.2% higher sample-level F1 score and a notable 6.2% increase in event-level F1 scores for SP detection. Furthermore, we established a smooth-pursuit experimental paradigm and identified significant differences in saccade and SP features between PD patients and healthy older adults through statistical analysis using the Mann-Whitney test. These findings underscore the potential of eye movement metrics as biomarkers for PD, thereby not only strengthening PD diagnosis but also enriching the intersection of computer vision and biomedical research domains.