Currently I have my fan rigged just to a switch so I can have it on whenever I want (mostly all the time).

To remind me, I'd like a LED to be on whenever the fan is off. Obviously this would be easier the other way, but I can hear the fan and don't need a light to tell me that it is on!

I have the LED and the proper resistor to bring the 12v down to the proper voltage.

Here is what I currently have:

 

Get a generic Bosch 30A relay and wire it in (for safety purposes too). It has an extra terminal that switches so it can send power to your LED when the fan is off and power to the fan when you turn it on. There is a diagram on the relay that should help in wiring it. Be sure and use a key on ign. source to power the relay or the LED will be on when the car is off.

EDIT
Just grabbed an old one. Here are the terminals and where to wire them:

85 key on ignition
86 fan switch (other end of switch goes to ground)
30 battery hot
87a led light
87 fan 12V hot

 

Much more convenient to use an SPDT switch than to use a relay.

 

A relay is the safe way to run a cooling fan. It just so happens he can have is cake and eat it to as far as the LED goes. I wouldn't want to run a 12ga. hot into the car to some mickey mouse radio shack switch for the fan, and neither did GM. All the wires stay under the hood except for a small ground wire that activates the fan. Simple and not fire-prone.

 

I meant for the LED, not the fan. No point running wires from a relay under the hood just for that.

 

To work with what you already have: move the fuse to the batt+ terminal, close to the battery. This is crucial for safety against fire.
Connect one side (-) of the LED to the wire between the switch and the fan, and the other side (+) to a wire (or a connection point in the fuse box) that has power when the key is on.