On your MY, the aux fan is controlled by the engine computer. It gets its input from the temp sensor in the rad outlet, and runs the fan based on coolant temp.
The engine computer tests the fan upon engine start. It spins it momentarily. I'm not sure if it tests on every startup, or just when cold. If it does not spin, I would suspect the fan controller, mounted on the fan shroud. Don't think the module is available separately.
I've not heard of you symptom before. You will need to get this diagnosed with a BMW-specific scan tool.
Have you examined the wiring from the fan to the e-box for opens or shorts? There s/b 12 V between the two heavier wires at the fan connector.