The light should indicate an error code with its flashes...

4 flashes - 3 second gap = short circuit
8 flashes - 3 second gap = open circuit

It is probably more likely to be abraded wiring or corroded connectors, rather than the sender unit itself. Start by getting the tank off and visually inspecting all the wiring and connectors associated with the circuit.

Next step would be to check the resistance between the green/white and black wires at the connector block on the pump body with no fuel and increasing fuel in the tank. You should either have very high resistance (no continuity) or very low resistance (continuity) depending on fuel level. I'd guess high resistance when the tank is empty and low when full, but it could be the other way round depending on how the warning lamp is wired.

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