Let me save someone some time in the future...
1979 M20J Fuel gauges reading half full when tank is full, but only after being drained.
I know this is absolutely the inboard fuel sending units being stuck.
It is not an electrical problem.
Here are some clues.
1) It is repeatable to almost exactly half. There are two sending units per tank in series. Assuming conservative failure of open circuit a wiring issue would tend to make infinite resistance and read empty, maybe a poor connection could read a higher-than-normal resistance. However, reading exactly half or 16ish gallons on a 32 gallon tank and having that repeatable. It is very suspect that a poor connection would be just the right amount of resistance for this indication.
2) It happens specifically when the tank is run very low or drained.
3) In my case when I drained both tanks that indicated full, and then immediately filled back to top, they suddenly both indicated exactly half full.
4) The number one reason I KNOW this to be a stuck sending unit is because a $32 amazon borescope wired tied to a 3mm aluminum wire from amazon allowed me to go in from fuel tank fill hole, find the sending units and touch the sending unit arm. Eureaka, arm popped up, did to the other side, both tanks full.
Should I replace the sending units? well, here are some thoughts. :
1) Conservative fail. It won't cause you to run out of fuel, only make an unnecessary stop.
2) Likely to resolve itself on your first sharp bank.
3) It's repeatable but ONLY by draining my tanks to the very bottom. If you don't drain your tanks to below 4 gallons you will not likely see this, and you should not be flying with 4 gallons of fuel anyway. E.g. calibrating a Garmin G3X touch to work with OEM sending units (btw they have to be in voltage mode not resistance mode even though they work via resistance).
4) I experienced this many years ago on the same aircraft (drained to flush tank) and a borescope on aluminum wire worked then too. 15 yrs later draining the tanks I had to purchase a new scope.
Note1 the inboard sending units are on a rod connected to a small circular panel bolted to the vertical inboard edge of the tank e.g. accessed from inside. I know this from looking inside the tank with a borescope.
Note 2 not changing the sending units is not about the cost of the unit, it's about opening up a can of worms by breaking a seal. Also my cal curves look very nice, I don't believe this is a problem worth the effort to fix at the moment.