Odd relay hook up question

Well its odd for me. Probably an easy answer for some of you guys. I have a 1993 Saturn SW2 that i just installed stock fog light into. I also want to use the stock switch. The switch operates and the wiring harness for it is already inside the car. But the underhood and lighting wiring harness and underhood fuse box do not have the option for the foglamps. So in order to make the stock switch work I need to make a relay system the turns on the lights when voltage is removed.

Basically there are four wires connected to the switch.

The output has 12 volts when the switch is off and no voltage when the switch is on.

-Mike

I don think so. I thought of that and tested to see if the output went to ground once activated. When I had the multimeter connected to the output wire and to ground the LED indicator on the switch was bright when the switch was on and dim when the switch was off. (the LED sould of been off). Also its an electronic switch and a toggle of anything like that, how could I rewire that? Is it possible? If its and easier alternative, I'm up for it. I'll see if I can get a wiring schematic of the switch to show you guys.

OK heres the schematic of the foglight switch:

My knowledge of schematics is very limited. Is "H" a positive or negative output?

H is supposed to be a negative output.  it's really a simple circuit - but i think you have it wrong.....  E should be high beam input, and F should be parking light input -- that way the light on the switch will only be on when the fog light switch is in the ON position, and the headlights are set to low beam (it's also the only way to make the fog lights turn on with the lights in low beam, but not high beam).  hook the switch up that way, and hook up this circuit under the hood, and you'll be set

errr..... doh  - what i should have said was, E should be the LOW beam input, and F should be the Parking light -- with E hooked to high beam, it would only activate fogs in high beam (duh) but the indicator light would be off.  anyhow, hook E to the low beam +  and F to the parking light +   G to ground and H to pin 86 on the above diagram, and you're in bidness

this is all of course, assuming that the transistor in the schematic you provided is an NPN (because it isn't indicated the normal way - like wiith an arrow on one leg). 

I guess I should come here more ofter and check replies. Thanks for your help. I'll give it a try.