I too have a dancing fuel gauge. And like others it quit working on the full side, but the low fuel lamp continued to work. And of course mileage method is always in use. I finally replaced the sender with the high hopes that it would fix the dancing fuel gauge with no joy either.
Jason, I'm sure that you are correct, your dash gauge is bad. I had the temp gauge do the same thing. I found out that they where sold as a pair and back ordered. So I took it apart, unwound the magnet wire, found the break and wound it all back together. Worked! Since then I have seen a lot of Rodeos with the same or similar gauges, I'm sure the fuel gauge from a junk yard Rodeo will work.
VXNewb, Do you have a picture of the back side of the fuel gauge that might show an added resistor, or more likely a capacitor? Wondering if it is a mechanical dampening that wears out, or if another component was actually added.