Temperature gauge is not working

This is normally a temperature sensor issue even if you don't have any codes. This normally only sets a code when the sensor or circuit fails due to an open circuit so the PCM is not getting a reading back. However, if the sensor is just wrong then it is displaying the temperature that the sensor is telling it so it doesn't know to turn a light on.

On more modern vehicles they have redundancies so to set a light for something like this but it doesn't appear this vehicle has those. I attached the testing below to determine if it is a sensor or not.

Here is a guide that will help with this:

https://www.2carpros.com/articles/how-to-check-wiring

Let's run through this and let me know what questions you have. Thanks