I doubt that the sender is at fault; it's just a pressure switch that opens the ground circuit for the oil light, and if it fails it usually results in a light not going out condition.
Since it pulses at low rpm, it's likely that the oil pressure is getting low either through a worn pump, main bearings not holding pressure anymore, or some debris in the bypass valve that's bleeding off some pressure by not allowing it to close all the way.
Swapping out the sender is the easiest and least expensive first step in the troubleshooting process though.