Mercury Sable 1996 Fuel gauge erratic how to repair it and what piece to buy ?

Here's a video on replacing your fuel pump. How To Install Replace Fuel Pump 1996 06 Ford Taurus Mercury Sable

Cathy, 1996 Mercury cougar gas gauge not working. Simplest thing to check first is your fuel gage fuse, make sure all fuses are good. The ground wire could be corroded/damaged, sending unit in tank faulty, fuel level gauge in cluster faulty. All things can be tested by a good Tech.,diagnosed and estimate for repair.
1994 Mercury Cougar gas gauge don work
Ford Gas Gauge Does Not Work Help Blue Springs Ford Parts Blog
Diagnose Fuel Gauge

if it is only the fuel gauge it will most likely be the sending unit in the gas tank.

change cluster 4 fuel gauge

MERCURY SABLE , manufactured by FORD MOTOR COMPANY had a problem with SUSPENSION:FRONT . AT HIGHWAY SPEEDS, VEHICLE SWAYS AND VEERS EXCESSIVELY IN MODERATE CROSSWINDS. *AK.Vehicle Identification Number (VIN):1MEHM55S31A. MERCURY SABLE 2001 problem was reported in ANDOVER, MA. Original Owner. Vehicle was purchased on 20000901. Vehicle was using ANTI-LOCK BRAKES.Vehicle was using Cruise Control.MERCURY SABLE 2001 drive type:FWD. FUEL SYSTEM:N/A. FUEL TYPE: GAS. VEHICLE SPEED: 65 mph.

most likely it is the sending unit in tank that is stuck 1/2 way and will not register.

the fuel filter is located on the right side frame rail near the corner of the fuel tank.

The fuel filter is on the passenger side of the car back close to the rear wheel, the fuel pump is inside the fuel tank.

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Check for spark. If you have spark and fuel, check for compression. You can rent a comression gauge from many auto part stores. Make sure you ask them for the compression specs. A compression test will reveal if there is a physical issue with the engine.

bad fuel injectors or dirty injectors if they are leaking it could do this