Fuel guage reading incorectly

I'm new to the Gen 1, but not necessarily the later version Priuses. About a month ago, the wife and I decided to trade our car payment on a loaded '13 Subaru Outback Limited, for a paid for with cash $4500, 2003 Prius with 92K miles on it.

Car was purchased at a very sketchy BHPH type lot (was the nicest condition car there of about 20-30 cars) Anyway all has been well in just over a month of driving the car and about 3300 miles logged. The 12v, Aux battery was dead from the car sitting on the lot for so long (I replaced with a new OEM Toyota 12v battery) After a week of the car experiencing dim headlights, and various other electronics (No codes or CEL though).

Now that the 12v battery has been replaced, the car runs exceptionally well, aside from an intermittent fuel gauge issue where it only reads full bars (completely full) if I let the tank get to empty (Flashing single bar) or close to that. If I fill the tank from say 1/2 or 1/4, or even 3/4 it will show one bar low, or sometimes two bars low. I have tried driving for 5-10 minutes to see if it was a leveling issue (sometimes it will cure itself and got to full) and others my wife says it will still show two or one bar low for her entire commute to and from work. I have even tried driving for say 5-10 minutes, then trying to pump more gas into the tank (won't let it, because tank is full obviously) only to find the gauge is still reading two or one bar low.

What's odd, is that if I fill up from almost or near empty, it will show full bars every time. Doing a little research, I have read there have been issues with the second gen fuel gauge, I hadn't heard anything regarding the fuel gauge on the 1st gen.

Anyway, has anyone else run into this issue with their gen 1? Any feedback greatly appreciated.

 

Ironically, I've ran a bottle of the techron concentrate fuel cleaner through the tank, just as a precaution when I first got the car.
I couldn't tell you if it has really helped, but truthfully I hadn't noticed the fuel level issue till two or three fill ups after the cleaner.
Perhaps the techron fuel cleaner was my problem. Thanks for the responses though so far.