Gmc - 1500 :: 2001 - Gas Gauge Always Register Empty When Fill Up The Car

I've got a 2001 GMC Sierra 1500 with about 80,000 miles and with a gas gauge that is possessed. It sometimes appears to be working normally, but is just as likely to do very weird things, like: When I fill up the car with gas, it will always register empty. And it will stay there until it sees fit to move to full. BUT: if, as I'm traveling down the road, I move the transmission from drive to neutral, the gas gauge will move to full. This also happens arbitrarily between fill-ups, with the gauge sometimes registering empty and sometimes finding some random place around where it should be. Once again, if I put the car in neutral, the gauge will move to its correct position (at least I think it's the correct position!). I was told my one mechanic that the problem is that the fuel pump is wearing out, and that this problem is not uncommon for the Chevy/GMC trucks. The fuel pump is in the gas tank, I'm told, so to replace the fuel pump is rather expensive.