Water temperature sensor? if canadian car it has an extra switch for water temp.
both us and Can cars have the sensors for water temperature just under the thermostat housing ( front of engine, right beside the valve cover ). you will have 3 or 4 sensor there, thermotime, water temp and one other, can't remember name right now
I do not have the book with me but I would assume that is where your getting your signal for the guage in the car. However, if your water temp sensor connection was bad then your car would run bad or not run at all, so I would lean towards the connection in the dash to the display?
I may be wrong though, never had that problem, nor knew anyone that did.
The following is for a 79, the location of the sensors may be different for an 81 but the description of what they do is correct
Looking at the motor from the front, the thermostat housing has the following items:
At 2:00 o'clock the "Water Temperature Sensing Switch". It controls the fan which blows air towards the injectors / intake manifold when the coolant temperature is above 110C. It has a single wire connected to it with a "male" bullet connector at the end of the wire. (it is usually green and about 2" long)
At 4:00 o'clock the "Water Temperature Sensor". It is connected to the ECU and provides coolant temperature readings in the form of a change in resistance. As the coolant temperature increases the resistance decreases. This sensor works in conjunction with the "Air Temperature Sensor" in the AFM and is also connected to the ECU. These two sensors provide input to the ECU so that the ECU can change the fuel injector pulse width.
At 8:00 o'clock the "Thermotime Switch". It is connected to the "Cold Start Valve".
At 10:00 o'clock the "Thermal Transmitter". It is connected to the Temperature Gauge in the Dash. It has a single "male" bullet connector built into the end of the sensor.
the sensor that you want is the one on the top left closest to the valve cover facing the front of the engine. It is the one that has the single bullet connector coming from it, that is the one that operates the gauge on the dash.