Fuel level sending unit

My gas gauge was under half tank yesterday but while I was driving last night I noticed it was moving up and down as I stepped on the gas. I parked on a hill and it went to full. I was wondering if the fuel level sender should be changed and can I get to it from the trunk. I have an 04 grand prix. I've noticed if I lift the rug in the trunk there is a silver plate in the center rear or trunk and a gold one off to the left with wires coming from it

Yes, its replaceable.

The bigger silver one is for the fuel pump access.

Youtube. "bonneville fuel level sensor replacement" , Its a 3 part video on how to do it.

97-03 the ebay part is like 20 bucks. I have not looked at a 04+ one, but it cant be much more.