Assuming the fuel gauge system is the same in your J as the K, if it reads empty with the master off, it is almost certainly the wiring to the tank sensors or a tank sensor itself at fault. 12v power goes to the gauge and the other wire on the gauge runs out to the tank. The tank has two sensors, one on the inboard side and one on the outer end. The inner gauge is insulated from the tank. The wire from the gauge runs into the inner sensor and on through it to the outer sensor, where it goes through the sensing element and to the ground. The net effect of this is that the average reading between the two sensors is received by the gauge, which theoretically gives an accurate reading regardless of the roll attitude of the plane.
What you are most likely seeing is that the wiring is getting to a ground somewhere. The most likely spot is the sensor on the inboard side, where the screws holding the sensor in the tank has insulated washers. If one of those fails, the voltage runs directly to ground and tells the gauge the tank is full.
If you are reasonably good tracing electrical, this is not a tough one to find. If not, anyone with knowledge of how the system works can do it relatively easily. Removing the side panel under the door (or in the anagalous spot on the pilots's side) will give access to the inner sensor. To access the outer one, you have to take an inspection panel off the underside of the wing just past the end of the fuel tank. It is a little tight in there, but not too bad.
If I can help, send me a PM or call.
Don 214 207-6744