My fuel gauge reads full all the time. While I wish what it said was true, what should I check first to find the problem causing the overly optimistic reading?
You may want to check the ground connection at the sender - this is often one of the causes when senders give a false reading.
Recently, we had to replace the sender for our NH TC40D - it had rusted to the point that it no longer had free movement and tended to stick and give a false reading.