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This vehicle uses two seperate sensors, one for the guage and one for the computer. So it sounds like the one for the guage is working but the one for the computer needs to be replaced. Here are instructions to replace if that does not work you will need to check for resistance, open wire, or shorts between sensor and computer. Let me know if you have questions, thanks.
Initially you said there are two temp sensors--one for the gauge & one for the computer. You implied with your text portion of your answer & showed with the instructions that the coolant temp sensor for the computer is located next to the thermostat housing. My second question is "Where is the sensor for the dash gauge? Your answer to my second queation is "The engine coolant temperature sensor is located next to the thermostat housing." Are you now saying there is only one engine coolant temperature sensor which is for the computer & the gauge, or are you not understanding my second question which is--Where is the engine coolant temperature sensor for the dash gauge?
If there are two separate coolant temperature sensors, & the one for the computer input is next to the thermostat housing, "where is the engine coolant temperature senor that provides the signal for the dash mounted temperature gauge?
One is a temp sensor one is called a temp sender. Here is a picture location and replacement instructions. Let me know if you have questions, thanks.
Here are wire diagrams but since you said the guage works like it should I think the problem is the engine coolant temp sensor or possibly the wiring. You can monitor resistance with engine cold and start engine as as the engine warms up the resistance should steadily change if not replace. Let me know if you have questions, thanks.