Newbie & tech question

Hi all. New to the forum, and new to Aprillia. My name's Laurens van Deijk. Boring screenname is easy to remember (computer login). Bought my first Aprillia 3 months back, very happy since. Tuoldo, grey/red, 2004. Loads of carbon, very slick.

Owned all sorts of bikes. BMW, Yamaha, Suzuki, Honda. Mostly BMW though, loved the old GS.

Few weeks back did my first own maintenance on the Tuoldo. Except for the hard to reach righthand sparkplugs it's a breeze. Am having some problems with the fuel indicator though, and before ripping the unit out wanted to check here if it sounds familiar. Indicator light stays turned on, no matter enough fuel or not. Check the cables, couldn't find anything special. Resistance thingies (don't know the english word > relais) all seem in order. Couldn't find much on the boards. Is the fuel sensor one of those dodgy parts in general?

Cheers.

Not sure, previous owner told me that he never had any problems with it. When I bought the bike problems magically appeared. :yes lol
Have been doing some research how to dissassemble the fuel pump unit. Will check the wiring, can't imagine it's the sensor itself.
I'm more of a Stella Artois guy myself. What's that saying? Grass is always greener....

Picca of the bike:

Took the thing apart yesterday, couldn't find anything special. Hoping it's just a trapped wire, taking it out for a spin this afternoon.
It looks like a nice late-summer day here in the Netherlands. Sun & comfortable temp.