Nick - As said in your introduction post, check out the Troubleshooting tab on our page at Documentation/Electrical/
Gauges.
But fuel gauge sending units are notorious for going bad. So many of us have had problems.
To your specific observations, the gauges don't show anything meaningful when the key is off. As explained on the Troubleshooting tab, the gauges are actually thermometers and have a heating element below them. So what they show with the key off is more related to the inside temperature of the truck than anything else, but a fuel gauge will usually show below Empty a few minutes after the key is turned off.
So if yours shows above Empty then the gauge may be bad. And if it goes to the same place for either tank with the key on that might also suggest it is bad. But the real test is, as suggested on the Troubleshooting tab, to pull the wire off the sending unit and ground it to the frame. Then get in the truck and turn the key to On. In a few seconds, as the gauge heats up, it should read above Full.
Don't leave the key on too long as it might hurt the gauge, but you can flip the tank switch to the other tank and if its wire isn't grounded it should slowly drop back to read whatever level is in the tank, which you said is Full.
Gary, AKA "Gary fellow":
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Dad's: '81 F150 Ranger XLT 4x4: Down for restomod: Full-roller "stroked 351M" w/Trick Flow heads & intake, EEC-V SEFI/E4OD/3.50 gears w/Kevlar clutches
Blue: 2015 F150 Platinum 4x4 SuperCrew wearing Blue Jeans & sporting a 3.5L EB & Max Tow
Big Blue: 1985 F250HD 4x4: 460/ZF5/3.55's, D60 w/Ox locker & 10.25 Sterling/Trutrac, Blue Top & Borgeson, & EEC-V MAF/SEFI