Is it really a 120V fan in a 240V heater? Check that.
I don't know how accurate this would be as there would be a delay going both on and off line.
One other way I can think of to do your job without butchering the POW is to use an external 120V relay between an always powered POW and your light bulb load. In other words wire up a POW to an always on hot and neutral with a light bulb as the load and turn it on. In series with the light bulb circuit place the NO contacts of an external relay. Connect the 120V coil of the external relay across your fan motor circuit such that the relay energizes when the fan motor comes on. When the external relay contacts close your light bulb will light and start drawing current through the POW.
You will want to select a 120V relay with a continuous duty rating.