How to power 12V fan and 3V LED with a 9V battery?
Assuming your fan will reliably turn on as you state, and assuming your battery can supply enough current for the LED and Fan, this will provide the functionality that you need.

1 - When battery is connected, LED lights up.

2 - When battery is connected and switch is turned on, FAN will turn on.

The 330R resistor you said you have should give about 20mA for most LEDs.







simulate this circuit &ndash; Schematic created using CircuitLab