2011 Ford F150 5.0L Engine: Transmission Temperature Sensor Malfunction and Failure Code Diagnosis

I'm experiencing a recurring powertrain fault on my 2011 Ford F150 with the 5.0L V8 engine. The transmission temperature gauge is behaving abnormally. When the truck is cold, both engine and transmission temperatures appear to rise together as it warms up. After driving for about two hours and stopping to run errands, I notice that upon restarting the engine, the engine temperature reads normally, but the transmission temperature gauge shows a 'cold' reading. After letting the engine idle for approximately two minutes, the transmission temp stabilizes and shifting returns to normal. If I exit the vehicle before the transmission temperature gauge reaches normal levels, the dashboard displays the wrench icon, indicating a failure mode. Repeatedly cycling the ignition (run to off and back on) about 10 times triggers the Check Engine Light (CEL), and after that, the truck shifts normally. However, this CEL clears after approximately 30–40 miles of driving, and the issue does not reappear until the next restart. I've already cleaned and disconnected all accessible sensors, but the problem persists. Ford has advised that the transmission temperature sensor is integrated into the valve body and costs around $700—this seems unreasonable for a diagnostic fix. My question: What is the color code for the transmission temperature sensor wires? And where exactly are they located for proper testing? Thanks in advance for any guidance or troubleshooting tips.