led w/ diode for electric fan

I recently put an electric cooling fan in my truck.  I have a LED wired in as an "on" indicator light.  I discovered that the air speed will turn the fan, when it isn't under power, enough to make the LED light dimly.  I know I can put a diode on the fan to prevent back feed but it would be easier to access the LED.  Can I put a diode on the LED to accomplish the same thing?

99 Chevrolet Silverado

I would put the diode stripe to the positive side of the LED right?

No - it won't stop current to the LED.... I thought you would place the diode across the fan terminals to dynamically brake it (else a resistor). But that is why people run the LED either from the relay's solenoid/trigger source, else they use changeover relay(s) for the fan(s) - ie, #30 to the fan; #87 from fuse battery; #87a to GND.

Thanks.