Had a similar problem recently and fixed it over Christmas, forgot to take a few pictures.
As most may know it uses a potentiometer which changes resistance as the level of fuel drops. It has a small levers which rotate across a resistive track to change the resistance. Sometimes the tracks wear or the lever wears in the holder.
I removed the sender unit and the bar which holds the float felt like it had to much play on the potentiometer side. This is held in place with a spring washer with a washer under it.
Using a pliers I pushed the spring washer down more to tighten it up and it appears to have resolved the problem.
You were right.
One of these needles wasn't touching the contact board, due to loose washer.
I fixed it now, but more importantly, I think I know what caused it to get loose.
The bar which holds the float is on easy spot to get hit by fuel pistol while refueling, so, if you insert the pistol too low, you'll probably hit it and step by step cause further loosening of the washer.
I advise caution when inserting the pistol to avoid that...