P0480 Fault Code in 2006 Hyundai Azera 3.8L: Diagnosis and Fix After Replacing Fan Control Module and Relay

I'm experiencing a P0480 diagnostic trouble code on my 2006 Hyundai Azera with a 3.8L engine. The vehicle overheats during slow driving or at stop signs, indicating a cooling fan issue. I replaced the fan control module — this did not resolve the problem. I also replaced the fan control relay — no improvement. I inspected all wiring harnesses for loose connections, burns, or damage, and found nothing amiss. To test functionality, I bypassed the fan control module by directly connecting a manual on/off switch to the cooling fan. After disconnecting the battery during this process, I started the engine. The check engine light turned off initially, but when I shut down the engine and restarted it, the check engine light reappeared. I then drove 50 miles with the A/C on and the manual fan switch engaged — no overheating occurred, and the check engine light remained off during this period. After shutting off the engine, I left the fan running for a few minutes before restarting. The check engine light came back on immediately. I repeated the test: disconnected battery, turned on the fan via the manual switch, started the car, drove 50 miles with A/C and fan on — no overheating, check engine light stayed off throughout. After turning off the engine and switching off the manual fan control, I restarted the vehicle. When I turned the manual fan switch back on and engaged the A/C, the car did not overheat during the drive home — the check engine light remained on. Key observation: The engine can start without either the fan control module or the cooling fan connected to the battery, and the check engine light stays off. However, once ignition is turned back on, the check engine light returns. I previously purchased a new fan control module from the dealer, but it failed when installed on another 2006 Hyundai model — confirming that the issue isn't with the module itself. What could be causing this behavior? Is there a wiring or ECU communication fault related to the P0480 code? Any insights or troubleshooting steps would be greatly appreciated.