The response of a position-sensitive Li-glass based scintillation detector to focused beams of 2.5 MeV protons and deuterons has been investigated. The beams were scanned across the detector in 0.5 mm horizontal and vertical steps perpendicular to the beams. Scintillation light was registered using an 8 by 8 pixel multi-anode photomultiplier tube. The signal amplitudes were recorded for each pixel on an event-by-event basis. Several pixels generally registered considerable signals at each beam location. The number of pixels above set thresholds were investigated, with the optimization of the single-hit efficiency over the largest possible area as the goal. For both beams, at a threshold of ~50% of the mean of the full-deposition peak, ~80% of the events were registered in a single pixel, resulting in an effective position resolution of ~5 mm in X and Y.