Hi,

I’m a 240 man and I don’t anything about the 444-544 but a fuel gauge is nothing more than a DC heating element attached to some metal that warps and that moves the needle.

You are getting too much current through to the heating element.

There is a voltage regulator some where that supplies a voltage less than the cars nominal voltage so it always gets the same potential to heat the element the same despite voltage fluctuations in the rest of the car.
It could have gone wacko as it should hold the voltage on the instrument cluster at approximately 9-10 volts.
In your age car it is probably a mechanical type that has points that open and close rapidly as it heats.
If you can take a voltage reading you will see it constantly moving the voltage up and down in that 9-10 volt range. Solid state devices hold it the same with less swing.

Now, 🙃 there is a twist to all of this! 😊
As the temperature gauge operates with same principles the VR will affect it as well since both are on the same controlled circuit.

(1) How is it doing?

So if it’s only the fuel gauge knocking the noggin, then you may have a wiring issue with the fuel gauge harness letting current go to ground and not through the sender’s variable resistance arm.

Since you have a used gauge you can play with the float arm and see this action with an ohmmeter.
Example might be as a 10 ohm to say 250 ohms is a range movement.
Full tank is the 10 ohms and the most current. Nearing 250 you’re empty. Float down.
On 240 there are tabs to limit the arm from going off the rails internally and giving you empty when it’s totally full until you use some fuel out of the tank.

You are only really caring if WHEN you are GETTING empty….. but staying full, I agree, is a toss up towards a worrisome worse! 🤭
On 240s there is an orange band for reserve observation at approximately two gallons left.
You calibrate the arm to that amount when replacing. It is used for “hunting up a fuel station” because with fuel injected cars you do not want to run either one of the two pumps dry!
Fuel sloshes about more while low and too low can start earlier in reality.
Down to one gallon is a thin amount spread over a few square feet of tank without adding slopes.

If the wires in between go to ground the fuel gauge will peg upwards. A broken wire makes the gauge read nothing.
There could be a bare wire in the harness touch another wire routing itself to ground or the wire is actually touching metal somewhere.
Test often when wiggling so if it moves and works you will have an idea the last place you touched.
We will discount to an improbability that you are managing to hang the arm up inside the tank each time.

(2) Have you tried putting the old sender on the harness and testing it all manually incrementally?
It’s not rocket science but patience can be rewarded.

Good luck and I hope I armed your hands through your head on “How it worked” with older vehicles.
The newer 240s use a solid state VR that can be used if you want. They should be cheaper than mechanical ones if they are even still made?

Phil