Hello and welcome

Not a clue about electrickery but google AI says the below - although it often talks bollocks.....
When a Ducati 821 cooling fan stays on after the ignition is turned off, it usually indicates a faulty
radiator temperature sensor, a
stuck fan relay, or a malfunctioning
BBS (Black Box/Body Control Unit). This persistent power draw quickly drains the battery, often masking deeper electrical faults. [
1,
2]
How to Diagnose and Fix the Issue
To stop the fan from draining your battery, follow these steps to isolate the fault:
1. Pull the Fan Fuse or Relay
While you are actively troubleshooting, immediately pull the fuse (usually 15A) for the cooling fan or pull the cooling fan relay to prevent your battery from dying while the bike is parked. [
1,
2]
2. Check the Radiator Temperature Sensor
The most common cause of fans running uncontrollably is a faulty coolant temperature sensor sending incorrect resistance data to the ECU. [
1]
- Action: Disconnect the temperature sensor and check the pins for corrosion or moisture.
- Test: If you have a multimeter, measure the resistance. If it is erratic or reads incorrectly, the sensor needs to be replaced. [1]
3. Inspect the Fan Relay
The fan relay can sometimes stick in the closed position, continuously completing the circuit to the battery. [
1]
- Action: Locate the relay (typically under the seat or near the battery box).
- Test: Unplug the relay and give it a tap. If the fans immediately stop when unplugged, the relay contacts have likely fused together and the relay must be replaced. [1, 2, 3]
4. Investigate the BBS Unit
If both the sensor and the relay are functioning properly, your Body Control Unit (BBS) might be shorted, keeping the fan circuit energized. [
1]
- Action: This is more complex and typically requires taking the bike to an official dealership to check for system error codes and flash the ECU/BBS software. [1]