Fuel gauge pegged means the sender isn't grounded. It could be the sender unit itself being faulty or corroded up but the easy things to check first are that it is even plugged into the trunk harness. The ground wire from the sender connects to the rear body underside below the filler cap. If there, unscrew and clean the metal and replace for a good grounding. You'll also see the fuel sender harness coming through the trunk back panel next to the filler cap and plugs into the rear light harness, the larger one shown in your pic.
As Brian said, the white wiring plugs are for your cabin dome light. It simply clips into that unplugged harness. If you have a trunk lid light it piggyback onto that and is orange, but was an option. Be aware that they may have unplugged the light for a reason. Usually when they start fiddling with LEDs or have grounding dramas due to faulty door trigger switches and the like.
