Posterior circulation stroke (PCS) presents significant diagnostic challenges due to poorly localizing and non-specific symptoms, such as dizziness, nausea, and headache, which are often misattributed to benign conditions. This study introduces an innovative diagnostic tool that utilizes a machine learning algorithm-driven eye tracker to enhance early diagnosis of PCS. Our approach involves analyzing eye movements during three standard neurological eye examinations: the Dot Test, H Test, and Optokinetic Nystagmus (OKN) Test. The Discrete Radon Cumulative Distribution Transform (DRCDT) and nearest subspace (NS) classification methods were employed to distinguish between PCS patients and healthy controls by identifying specific eye movement patterns. Results demonstrate that the ensemble model combining the three tests achieved the highest sensitivity and accuracy, with a sensitivity of 96% and an accuracy of 88%, in diagnosing PCS. This study's findings underscore the potential of an eye-tracker-based diagnostic tool to support a more accurate and efficient diagnosis, particularly for non-neurology trained providers, which would improve patient outcomes with more timely and appropriate treatment. The proposed tool offers a practical solution to the limitations of current diagnostic methods, such as the need for calibration and reliance on highly trained specialists, and can be seamlessly integrated into clinical settings to support emergency medical services (EMS) and emergency department (ED) triage.