defective fuel gauge

Yesterday after a fill up, my gas gauge started to work intermittently. It shows full, then after a while empty, then full again and so on.
I did not notice any correlation with the slope, speed or road structure.
I have no ODB error code detected neither.

The car is a 93 Aero from 12/2001.

I see on forums that the fuel sensor has to be changed.
Do you know if the fuel sensor on my model can be changed independently or if I have to change the entire fuel pump.
And would you have indications on the procedure to follow?

Many thanks.