Radiator Fan - Engage Temperature?

Hello, the cooling fan should come on roughly around 200f degrees, the thermostat on this vehicle should open at 194f degrees. Are you noticing the gauge rise higher than about half way after the engine gets to its operating temperature? There is a chart in service information where you can check the resistance of the sensor against the temperature the sensor is. I have seen engine coolant temperature sensors (ECT) being 15-20f degrees out of spec and not setting any codes like sensors should when they start failing. I'll post the chart for you to see.

This first diagram is the Resistance to Temperature Chart, so with a multimeter set on the Ohms setting, and the sensor unplugged, it should read the resistance for whatever temperature the sensor is at. So you would need to measure the sensor with some temperature measuring probe, but the sensor needs to be unplugged for this measurement. The other diagrams are the temperature sensor operations, and diagram 5 you can see the engine computer (ECM) uses that sensors measurement to operate the cooling fan relay.
Something to note, is any extra resistance in the two wires for the sensor, such as corrosion in a wire or connector will cause the sensor to read incorrectly. As the temperature of the engine goes up the resistance on the sensor goes down, so for example at 194f degrees the sensor should read 241 Ohms when checking on its two pins.
Using a scan tool can also help, checking the live engine data to see what the ECM is seeing for a temperature reading versus what a temperature probe is actually reading at the sensor can help to determine if the readings are accurate and the same.

Here is a guide to help understand how the sensor works:

https://www.2carpros.com/articles/how-a-coolant-temperature-sensor-works

https://www.2carpros.com/articles/how-to-use-a-voltmeter