Low indication means "low fuel" or the fuel float sitting low in the tank. If it is partially flooded, it will sink to the level of buoyancy, which is dependent upon the amount of fuel above and movement available. If true, you're a hair's breath away from it always reading zero.
When your tank is nearly empty, remove the sending unit and see if the float is able to rise up in a bucket of water with the sending unit frame oriented as though it was on the tank. It should rise to the surface of the water, regardless of water level. If it does, check for resistance across the sending unit: ~73 ohms at the lowest point, ~13 ohms at the highest point.