Let me explain what is actually going on here. Back in the day, when Pathfinders first came out, they had a secondary fuel gauge to monitor the reserve fuel left in the tank. Over time they phased out the secondary gauge with a little fuel light. Some say it was to discourage people from running low on fuel because it's bad for the pump. Now when Nissan replaced the secondary gauge with a light, they did this in a very lazy fashion. They literally just took out the gauge and wired a light into its place instead. When you see the light slowly come on, this is equivalent to the secondary gauge going down. In fact you can still replace that little light with a secondary fuel gauge. As the reserve dries out, the resistor decreases its resistance and increases the voltage to the light until the light glows bright, which means you are out of fuel.
Now with that in mind, corrosion on top of the sender can do funky things. Take that fuel sender cover off and take a look at that sender.