95 Pathfinder fuel gauge question

I did a search in the Pathfinder forum for fuel gauge issues, but didn't come up with an answer to this question. I'm sure I saw something about this somewhere in here before, but I can't find it now.

I'm pretty sure I know the answer, but I'm looking for some reassurance. My 95 Pathfinder LE (V-6, A/T) has a 21.1 gallon tank. I just bought this rig a few days ago, and it was reading pretty close to empty (maybe 1/8th tank) when I picked it up from the guy I bought it from. I didn't pay much attention when I filled it, but looking back at the receipt, I only put 12 gallons into it, and that was after topping it off. That means I had around 9 gallons left while only reading under 1/8th of a tank. Today the gauge read just barely over half full and I filled up again, this time putting in 6 gallons including top-off.

I'm guessing I have a fuel tank float switch (quantity indicator switch) that needs replacing, right? Or is there something else inherent with this car that I should be looking at first?

This was driving me nuts because I thought at first I was only getting about 10-12 mpg, but after realizing the gauge was off, I'm really getting around 19 mpg...much more acceptable!

Thanks all you Pathy guru's!

Mike