I just replaced the fuel pump for my 1996 3.8 Ford Thunderbird. The car will turn over and runs but now the gas gauge reads full all the time. I would probably say oh well and use the trip meter to tell when I needed to refuel but that was broken when I originally bought the vehicle. What steps do I need to take to fix this issue? I really don't want to have to buy a new pump.

this may help

It is stuck...have the sending unit replaced.

If he told you the fuel pump would correct the fuel guage, take the car back and make them fix it under warranty. I have been in the auto repair business for 21 years and if I mis-diagnose a car, I have to fix it for free to keep the customer happy.

A mechanic would check for voltage and ground at the connector for the gas tank. Could be the sending unit in the tank, the gauge on the dash, or a wiring problem.

This is one of two things, it could be the fuel level sender or a bad fuel gauge, a bad gauge would mean replacing the cluster,
I would run gas low and drop the tank, remove the fuel assm, the sender is the part that holds the pump, i will enclose a picture to show you.This being a 1996 Bonneville i would bet its the sender in the tank.i would change the fuel pump while you have the tank down. Also check wiring and connector as some of these pumps will tell you to replace the wiring and connector, this is supplied with the new pump.If you are replacing the pump also then replace the fuel filter.\The only problem is make sure you spray the line to the sender on the top side of tank and let soak. this is if there are rusted. in my area they are rusted on these older cars. good day. have enclosed the picture of the fuel pump and the sending unit . hope this is helpful.

Perhaps you might consider the sending unit in the gas tank.

Most likely it a bad fuel level sensor on you fuel pump. You will have to replace the fuel pump as that is the only way to replace the sensor for you fuel gauge. The sensor is built into the fuel pump. The contacts on the sensor become corroded over time and cause the sensor to malfunction causing your fuel gauge to read full all the time. I have a 2001 Montana extended version that had the same problem. In order to know when I needed to fill the tank, I would completely fill it each time I put fuel in and reset my trip odometer. I would go 400 miles on the tank before I would refuel until we were able to replace the fuel pump.

it is probbally the fuel pump in the gas tank. It has a float like the one in your toilet and a sensor attached to it to tell you how much gas you have.

More than likely it is the sending unit inside the fuel tank. You will need to remove the fuel tank and take the sending unit out of the tank and replace it.

This is a normal concern.
The instrument cluster uses 4 different operating modes to calculate the fuel level:
Anti-slosh (default mode)
Key OFF fueling
Key ON fueling
Recovery
After a fuel fill up, the time for the fuel gauge to move from empty (E) to full (F) ranges from 2 seconds to 55 minutes depending on which operating mode the fuel gauge is in.
The default fuel gauge mode is called the anti-slosh mode. To prevent fuel gauge changes from fuel slosh (gauge instability due to changes in fuel sender readings caused by fuel moving around in the tank), the fuel gauge takes approximately 55 minutes to go from empty (E) to full (F).
The key OFF fueling mode (2 seconds to read empty [E] to full [F]) requires 3 conditions be met:
The key must be in the OFF position throughout the entire refueling of the vehicle.
At least 15% of the vehicle's fuel capacity must be added to the fuel tank.
The instrument cluster must receive a valid key ON fuel sender reading within 1 second of the key being put into the RUN position. The key ON sample readings are considered valid if the fuel sender reading is between 15 ohms ± 2 ohms and 160 ohms ± 4 ohms.
If these conditions are not met, the fuel gauge stays in the anti-slosh mode, which results in a slow to read full (F) event.
The key ON fueling mode (approximately 90 seconds to read empty [E] to full [F]) requires 3 conditions be met:
The transmission is in PARK (P).
The key is in the RUN position.
At least 15% of the vehicle's fuel capacity must be added to the fuel tank.
In key ON fueling mode, a 30-second timer activates after the transmission is put into the PARK (P) position (automatic transmissions). When the 30-second time has elapsed and at least 15% of the vehicle's fuel capacity has been added, the fuel gauge response time is 90 seconds to read from empty (E) to full (F). When the transmission is shifted out of PARK (P), the fuel gauge strategy reverts to the anti-slosh mode. The key on refueling mode prevents slow to read full events from happening if the customer refuels the vehicle with the key in the RUN position.
Recovery mode is incorporated into the instrument cluster strategy to recover from a missing fuel level input during a refueling event. Missing fuel level inputs result from intermittent opens in the fuel sender or its circuits. Recovery mode (empty [E] to full [F] approximately 20 minutes) is initiated when the following 2 conditions are met:
The instrument cluster is in the anti-slosh (default) mode.
The actual fuel level in the tank is greater than what is being displayed by the fuel gauge