Hi, looking at the picture of the fuel sensor unit it looks as though the yellow and black wire go to a conventional variable resistor, sometimes a wire-wound one that connects to the float (that's how most sensors work). If this was worn or faulty it would create the very problem you are describing. It could be the wiper contact that's worn out, dirty, or bent out of shape.
The actual fuel gauge will just be an analogue meter and if it moves from zero to full, even intermittently, that would indicate that it was OK;they either work or not. Of course there could be a loose or dirty connector along the path somewhere which could cause a similar fault.
Not sure how much a complete new unit would cost but if that's the only problem with the car, as others have suggested, I'd go by the Trip Counter and fill up when necessary.
Mike.
