The CTS is in the neck of the thermostat housing. The gauge/light temperature sending unit is in the left front corner of the cylinder head, just in front of the thermostat housing. It's possible to swap places with them if the wiring harness has been messed with enough that the wires can be extended.
First, verify that your gauge is calibrated correctly. With no power applied, the needle sits on the bulb of the thermometer symbol. With engine cold and ignition ON, the needle should move to the 100 mark. Testing temperature with an IR thermometer, focus the beam on the brass base of the sending unit. It should be very close to the correct temperature. Verify your gauge agrees.