P0691 OBD2 Code on 2009 Saturn Sky Redline: Fan Runs Continuously After Module Replacement

My 2009 Saturn Sky Redline (2.0L turbo) developed a cooling fan failure about two weeks ago. I confirmed that the fan motor itself functions properly when powered directly with 12 volts. I replaced the fan control module, and the vehicle ran smoothly until yesterday, when a P0691 OBD2 diagnostic code appeared. The engine operated normally with the check engine light on—no overheating occurred. Today, after a brief drive where engine temperature remained within the 199–202°F range, I noticed the cooling fan is running continuously even when the ignition is off. This behavior raises concerns about potential electrical faults or sensor miscommunication post-module replacement. Any insight into resolving this P0691 issue on my Saturn Sky Redline would be greatly appreciated. Thank you, Allan P.