One more comment.
The damping and other things I have mentioned is true, and is the main cause for a different reading when you turn it off and on.
BUT, for the most part, it is NOT the cause for the needle to move at different rates depending on how much is in the tank.
The reason for that is in the sender and the shape of the tank.
The sending unit is basically a potentiometer. Same as the volume control on a radio.
At least the older radios.......
If you were to go to a electronics store and ask for a certain value potentiometer, hereafter to be known as a pot, because I am tired of typing the whole word, you would be asked what taper you wanted.
Pots come in different tapers. As you turn the shaft, or move the float in a gas tank, the resistance changes.
With a pot, you can have a linear taper, where it changes the same amount per degree of rotation from lock to lock, a log taper where the change is a log function, or an audio taper, similar to a log taper where the change is a function of the ear's audio response.
You would expect the sending unit to be linear. But that is hard to do, and costs money to make it accurate.
So, most sending units are "good enough".
But, there are other problems.
Think about how the arm moves on a sending unit.
When it is sticking out at right angles, a 1/4 inch drop in the level of the fuel, moves the float 1/4 inch.
Which moves the wiper on the resistor wire a certain distance. But, when it is hanging down at an angle, that same drop moves it a different distance, and moves the wiper a different amount.
So, if you want the output of the sending unit to be linear, then the resistor cannot be linear because the movement of the arm is not constant per amount of fuel movement.
Which makes designing the resistance wire even more interesting. If you look at the guts of a sending unit, the wraps of wire might be even all across the sweep of the wiper, or they may be closer together at different parts.
That is an attempt to make the output more correct.
But, even so, you would figure in these days of super computers, it would be a simple thing to design a wrap pattern, perhaps with different thicknesses of wire as you go across so as to make an accurate gauge.
And you could.
Except along comes the third problem.
Tank shape and size.
Check out the picture at the bottom. Its an extreme example, but as you can see, the level will change much faster towards the bottom per amount taken out than at the top.
Of course few gas tanks look like that, but they can have some strange shapes as car makers try to get more gas into less space.
They have all kinds of depressions, folds. Few of them are perfectly flat and square which would give a nice linear drop of fuel level per gallon used.
Add all of this together, and its a wonder we know how much gas is in our tanks at all.
Because, while mass production makes things cheaper, it also magnifies small amounts of cost.
So, while it would be quite possible to design a sending unit that will perfectly match the depth and shape of a gas tank, they would have to design and make different ones for every different tank out there.
You think getting the right bearing is hard? Imagine if there were different sending units for each model car and truck........
Even if you had two nice rectangular tanks which gave nice constant drops of fuel level, you would still have problems if they held different amounts.
The sending unit responds differently as the arm moves down, so if one tank was deeper than the other..........
So, does this mean you have to put up with a gauge that moves faster or slower as the tank runs out?
If it did so from the factory, you probably do. But, if it has gotten worse either gradually or suddenly, it might help to replace the sending unit.
They do wear out.
Or, if it reads normally until a certain point, when it just drops to empty even with gas left, then the last part of the resistor wire has broken and replacing it will fix the problem.
I know this is long, drawn out, and boring, but I was waiting on a phone call, and could not proceed on a project until I got it.
Got it now, so I'm out of here........
