diditanole,
I think I've seen this problem mentioned on here before. I'm guessing your dash light is connected to the load side contact on the relay. When the thermostat calls for 'cool', the relay closes, powers the fan AND lights your tattle-tail dash light.
If air passing through the radiator spins the fan, the motor turns into a generator, and through that connection on the relay powers your tattle-tail light.
You might have to add another light in series to act as a resistor, or add a resistor...or power your tattle-tale light off off the coil on the fan relay. Powering it this way wouldn't be 100% like it is now but unless you are a real unlucky fellow, should be 99% fool proof.
There could be someone along soon with a much simpler solution, lets see who pops in.
Stuart