The analysis of eye movements has proven valuable for understanding brain function and the neuropathology of various disorders. This research aims to utilize eye movement data analysis as a screening tool for differentiation between eight different groups of pathologies, including scholar, neurologic, and postural disorders. Leveraging a dataset from 20 clinical centers, all employing AIDEAL and REMOBI eye movement technologies this study extends prior research by considering a multi-annotation setting, incorporating information from recordings from saccade and vergence eye movement tests, and using contextual information (e.g. target signals and latency of the eye movement relative to the target and confidence level of the quality of eye movement recording) to improve accuracy while reducing noise interference. Additionally, we introduce a novel hybrid architecture that combines the weight-sharing feature of convolution layers with the long-range capabilities of the transformer architecture to improve model efficiency and reduce the computation cost by a factor of 3.36, while still being competitive in terms of macro F1 score. Evaluated on two diverse datasets, our method demonstrates promising results, the most powerful discrimination being Attention & Neurologic; with a macro F1 score of up to 78.8%; disorder. The results indicate the effectiveness of our approach in classifying eye movement data from different pathologies and different clinical centers accurately, thus enabling the creation of an assistant tool in the future.