The 1995 Lincoln Town Car coolant temperature gauge sensor can be found on the front of the engine. The coolant temperature sensor will be a few inches above the thermostat housing.
The computer uses the coolant temp sensor which is located near where the upper radiator hose hooks to the engine.
Fan Relay
The engine coolant temperature sensor and coolant temperature sensor are the same.
It is in front of the radiator.
Mid point of the gauge.
thermostat
Chances are not the temp sensor. It could be a thermostat or a hose that has a leak. And the one you dare not want it to be is a crack head.
It is behind the front bumper, in front of the radiator.
The coolant temperature sensor is screwed into the engine, behind where the upper radiator hose attaches. That is the main sensor the computer uses to run the radiator fans.
You will need to purchase a Haynes manual from one of the parts stores. You have to disconnect the coolant temperature sensor. Set the timing to factory specs and reconnect the sensor.
It is just below and behind on the area where the upper radiator hose attaches to the engine.
I have a 97 with 170000 miles. had the same problem. it was the WATER PUMP, the finns wore off!