It's possible it could be a problem with the Fuel Sending Unit.

If you do a search, there has been much written about the FSU on here over the years. There was a recall on that part a number of years ago. I think the 2002 might have been included with that recall.

It might be worth taking a look at the part and see if some corrosion has started to develop.

I'm sure others will chime in with suspected causes for the problem.