I wonder if oil-lit actually existed until later. To have gas meant you were on a, generally urban, gas supply, which normally had electricity close to hand by BR times. If the station was still gas lit it was more because they had not got round to updating it. Country stations might well have neither.
I can certainly remember stations in Somerset being oil lit in the 1960s. Yeo Mill Halt, on Taunton-Barnstaple, was the last I recall. Halts, with no staff, would require some way to turn them on and off, sometimes by a porter from an adjacent station travelling to and fro, sometimes by the guard on the last train. If there was a reliable regular passenger on the last train the guard would maybe give them the nod to do the work instead on their way out, saving them
time and the effort. Country people still had a good understanding then of what to do with oil lamps.