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The fuel level may not display due to various reasons: poor contact on the instrument panel, broken wire (corroded connection), lost ground, missing capacitor on the sub-distributor (behind the instrument panel). And one of the options is that the float doesn't work.

It's very easy to check — measure the resistance with a multimeter. It is measured in kOhms and should change when the float moves.

There isn't much that can break inside the sensor, except maybe for a broken coil. In this case, you need to find another one. But most likely there will be poor contact in the bushings. You must thoroughly soak it in orthophosphoric acid and clean it. Most likely, it's just a layer of corrosion or rust.