Check for a good ground between the tank and body. The sending unit needs a good ground to work (and with the tank undercoated (usually) and the pad on the top it is "floating" relative to the body. That is part of the reason why they use a strap between the fuel line.

On my '66 I added a screw in the edge of the tank and drilled a hole for a sheet metal screw to the frame for a good ground.

Also check the ohms between the sending unit and the housing of the sender. It ranges from about 10 - 100 ohms (I do not remember the exact values but somewhere around there).