2002 FX4 4.0 sohc. Trying to figure out which of the sensors are for the temp gauge. I know one goes to the PCM and the other to the gauge. Circled in the pic from when I change the timing components. They are push in style sensors and trying to figure out the correct part number has been a rabbit hole, not sure if it’s the brown or grey connection. Thanks in advance.

 

The single-wire sensor goes to the instrument panel gauge. The two-wire (plus ground) gauge goes to the PCM, and is the one that is actually sensed for engine coolant temperature.

It is reported to have a strange 'multi-phase' voltage curve that isn't intuitive to read simply by looking at the voltage coming out its 'sense' lead. Further if you wish to monitor its voltage, you must use a high-impedance device to read it, so as not to disturb the value of output going to the PCM.
LS