If yours is like mine, it's a pressure sensor tube that sticks down into the tank. When the tank level rises above the bottom of the tube, air pressure builds inside the tube and the pressure sensor switch turns on the light. Sometimes the tube itself becomes corroded by the tank contents and develops a small hole so air escapes instead of building pressure and they won't turn on. Since your light is staying on, it must be that the pressure switch is stuck.
I had to replace mine with the Snake River tank gauge system. You just screw out the 3/4 full tube and screw in a full length sealed PVC tube with sensors inside that never touch the tank contents, and it reads out tank levels in tenths. I have found it to be very accurate. The same display reader can handle your fuel and fresh water tanks too.
Doug Shuman