Never seen this flavor of problem on here before. 1970 Olds 98. Fuel gauge reads between 1/4 and 1/2 no matter how much gas, ignition on/off, battery connected or not. It appears to move a hair one way or the other now and then. Removing sender ground does nothing. Disconnecting brown wire from sender does nothing. I took the gauge out and applied 12V one way and it went to full. I reversed the wires and the needle went to empty (so the gauge appears to work). I put the gauge back in with the needle on full, turned on the ignition and the needle dutifully moved to its normal position between 1/4 and 1/2. I put the meter on the disconnected brown wire coming from the sender and there was no resistance between the brown wire and ground (meter pegged to no resistance). The tank is almost empty. There is no resistance between ground and the other side of the brown wire connector. All three leads on the cluster connector to where the gauge is seated appear to be fine (printed circuit board OK). Non-sender side of printed circuit board is supplying 12V to gauge.

So far, it looks like the sender is bad since measuring between the brown wire and ground shows no resistance, right? But if that is the case, the gauge should peg full, right?

I measured resistance between the non-tank side of the brown wire connector and the cluster plug behind the dash. There was no resistance between the plug and connector in the trunk (the sending wire is good). Interestingly, the sending wire also has no resistance between the connector in the trunk and several other pins on the gauge plug (like the pin for the oil-pressure light).

Any advice what I am missing here???!!!???

 

Sounds to me like the float on your fuel sender is stuck or seized in place.

 

Yep. Stuck float.
The design of the 65-70 big car sender encloses the float in a metal "can" with little clearance between the float & can. Either something rusted & it stopped moving, or the float is cocked or otherwise stuck in the tube.