The Faria wiring diagram indicates that all you have to do to find the air sensor is to follow the only red wire from the back of the gauge. The red wire will eventually connect to a white wire from the sensor.
I'm keen to check my Fairia gauge and follow the wiring at the back. The sensor is probably a thermister which is a type of resistor whose resistance varies significantly with temperature, more so than in standard resistors. A very simple device, worth about a $1 and easy to replace if you can match the impedance of the replacement with the old.
Update: I checked my installation. My Faira depth gauge only has 4 wires at the back. Two for the transponder and two to power the gauge. I'll never know where the air/water temperature senders may have been if the manufacturer had installed them.