Caribe, normally you are right on top of electrical, but you're having a major brain fart on this one.
The circuit that you drew putting a ground on pin 3, has the relay coil feeding 12v to pin 2, closing the switch connects it to pin 3, grounding the relay coil.
That will work.
But the ground on pin 3 is grounding one side of the LED.
Pin 7 grounds the other side of the LED.
May as well connect both ends of the LED to the chassis, the current is not going to flow through the LED.