An Oculomotor Brain-Computer Interface (BCI) records neural activity from regions of the brain involved in planning eye movements and translates this activity into control commands. While previous successful oculomotor BCI studies primarily relied on invasive microelectrode implants in non-human primates, this study investigates the feasibility of an oculomotor BCI using a minimally invasive endovascular Stentrode device implanted near the supplementary motor area in a patient with amyotrophic lateral sclerosis (ALS). To achieve this, self-paced visually-guided and free-viewing saccade tasks were designed, in which the participant performed saccades in four directions (left, right, up, down), with simultaneous recording of endovascular EEG and eye gaze. The visually guided saccades were cued with visual stimuli, whereas the free-viewing saccades were self-directed without explicit cues. The results showed that while the neural responses of visually guided saccades overlapped with the cue-evoked potentials, the free-viewing saccades exhibited distinct saccade-related potentials that began shortly before eye movement, peaked approximately 50 ms after saccade onset, and persisted for around 200 ms. In the frequency domain, these responses appeared as a low-frequency synchronisation below 15 Hz. Classification of 'fixation vs. saccade' was robust, achieving mean area under the receiver operating characteristic curve (AUC) scores of 0.88 within sessions and 0.86 between sessions. In contrast, classifying saccade direction proved more challenging, yielding within-session AUC scores of 0.67 for four-class decoding and up to 0.75 for the best-performing binary comparisons (left vs. up and left vs. down). This proof-of-concept study demonstrates the feasibility of an endovascular oculomotor BCI in an ALS patient, establishing a foundation for future oculomotor BCI studies in human subjects.