I am surprised the fan control module didn't pop up in your search. I believe i have read that is really common on the v6 and makes the fan run all the time.
Yes, it is integrated into the cooling fans on the Mk.2. If I remember correctly it is hardwired to the driver-side fan. It can however be replace separately but you still need to pull the fans to do it. The job is not a straightforward one [sigh]I have done some additional research and on second generation Mazda 6s the control unit is part of the cooling fan, unfortunately meaning the whole fan unit needs to be replaced.