Several studies have demonstrated that irregularities in eye movements represent an important indicator to diagnose diseases affecting the central nervous system. In fact, abnormal horizontal and vertical eye movements play an important role in measuring the progress of neurodegenerative diseases. Electro-oculography (EOG) is a widespread technique that monitors the horizontal and vertical eye movements in response to a visual stimulation pattern. These visual stimuli require stimulus-response synchronization, low latency, and a real-time response. In this work, a novel system based on a Field-Programmable Gate Array (FPGA) is designed to address hundreds of LEDs for the generation of multiple visual stimulus signals and for EOG acquisition. Our evaluation demonstrates that the proposed system enhances the accuracy of the signals generated, showing excellent results in the stimulus-response synchronism and quality of the stimuli waveform.