Other than the ammeter which is polarity sensitive, the other 51-6 gauges are bimetal or thermal style so all they care about is the regulated voltage supplying them and the resistance values of the senders.
As long as the stock instrument regulator is installed, it is also thermal. A heater causes a bimetal element with a set of contacts to open and close & provides an output of short bursts of 6 or 12v on and then off in a repeating cycle. Because of the slow response of their thermal elements, the gauges don't show the choppiness of the voltage and polarity will make no difference. Measuring the average of the output with a proper and decent meter, the value is around 5v.
If an original has been changed to an aftermarket or more modern replacement instrument regulator, some of those are solid state and polarity will make a difference. Depending on whether they are protected against polarity errors, they will usually not work at all or burn up.
Your symptom sounds a lot like the phenolic or fiber support in the sender that holds the resistance element has warped or wiper or a contact area has oxidized. When the wiper reaches that spot, the resistance value either opens completely or increases enough to mimic an empty tank. Warping is a common problem and some have also pulled their somewhat working senders out and found them so rusted, corroded or oxidized that it's a wonder there was any response from them.
Thanks for the information. It was very educational. I went ahead and ordered one of the sending units mentioned at the begining of this topic and am very curious to see the condition of my original when it comes out of the tank. Thanks again.