No need to remove anything until you determine if it,s wiring, the gauge, or the sender.
1) jump the "S" (sender) terminal on the gauge to the "G" (ground) terminal with the key on.
2) The needle should jump to full. If it doesn't go to step 3). If it does, the problem is the pink wire going to the sender or the sender itself. Now is the time to locate the sender.
3) Ensure there is 12 volts on the "I" terminal of the gauge and that the ground terminal is indeed grounded.
4) If there is 12 volts and ground at the gauge and step 1 didn't make the needle go to full you have a bad gauge.
5) If the gauge pegs full when tested, repeat this test by shorting the pink wire terminal at the tank to the metal shell of the sender. If the gauge still doesn't peg to full, the pink wire is broken between the sender and gauge or the metal shell of the sender is not properly grounded. If it does peg full, the wire is good as is the sender shell ground..
6) Now disconnect the pink wire at the gauge or at the sender. Using an ohm meter, measure the resistance between the pink wire terminal and the metal shell of the sender. Depending on the amount of fuel in the tank it should read somewhere between 30 and 240 ohms with 110 representing about half full. If you get no resistance reading or grossly erroneous reading, the sender is bad.