I don't know about the stop light coming on when you hit the accelerator, but the missus has a 306 1.9 diesel, the fan can run with the key out of the ignition, therefore if it stays running all the time, you know to replace the temperature sensor on the radiator to the right hand side of the radiator under the top hose, disconnect the electrical plug first, then use a spanner to undo the sensor, take sensor to car shop and buy it's equivelant (recommmend eurocarparts or gfs) type in on search page they have web sites much cheaper than peugeot's or halfords and better quality. Refitting is reverse of removal.
Don't forget to top up the coolant.
Good Luck
Lee
August 2007