Fuel gauge reads full all the time,and we did install a new sending unit with new fuel pump

power goes through the gauge down to the sender unit ,through the resistance to ground
what you have indicates a short in the wire after the gauge and before the sender unit

The fuel gauge is directly controlled by the fuel sending unit inside the fuel tank, it sends a ground return signal back to the fuel gauge. I am assuming of course that your fuel gauge is okay. To test your fuel gauge, connect the wire which goes to the fuel sending unit to chassis ground. Your fuel gauge should respond and indicate Full Tank. If not, there is a broken wire somewhere between your fuel gauge and the sending unit. Before connecting the wire that goes to the sending unit to ground, check it first with a DC Voltmeter, you should be able to read +12volts. Be sure that you turn your ignition switch to it's ON position.

Check for a frayed wire touching metal and grounding out. The gauge works on resistance and it registering full indicates a short to ground. Either that or your gauge itself is bad.

You change the sending unit

you have a float arm in the tank that rises when you add fuel I think its called the sending unit in the tank with fuel pump. it could be getting defective or it could be you fuel hand gauge going defective.but biggest part of time its the sending unit in the tank, hope this helps

if it worked for a short period of time after doing the pump/sending unit the check the connections going to the pump/sending unit they would have been moved around doing the pump

this is caused by a defective gas gage sending unit, the sending unit is part of the fuel pump module inside the gas tank, the gas tank must be removed to replace the fuel pump module that also contains the sending unit.

the sending unit is a variable resistor(potientiometer ) on the fuel pump
its probly bad it requiers a couple confirmation tests prier to dropping your gas tank and changing the pump but I got my money on that sending unit 97% of the time new fuel pump will fix it you coul change just the sending unit but you still have to pay almost as much and its the same job smartest thing too do is change the whole thing

sending unit on fuel pump is bad, the sending unit shorts out gauge will go to empty or full, never read right, turn on switch ,it goes to full or empty, ,check the pump,hope this helps,thanks robert b.

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