Hi there,
I'm chasing this same issue with the tiny bulb in the hazard switch. This is thread has great troubleshooting information!
The incandescent light didn't work when I bought the car, but was not burned out. I have a red LED replacement. I was able to fix the bulb's connection in the switch using the information above, so that it now lights with an external 12V on the correct pins. I verified the ground works on the connector, and both fuses are good. I'm currently verifying the the red/orange wire has 12V, as it still doesn't work when connected to the car.
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A couple questions:
1) What is the normal operation of the bulb that I should look for? I.E. Does it light up and stay on with the key on accessory? Does it only light when the switch is on? Does it blink with the operation of the hazard lights when they are on?
2) What is the function of the blue square in the picture that is located between the bulb and the area the lights up on the knob? Is it a diffuser, reducer, or what? With the LED installed, it seems to completely block the light!
3) Is there a VIN specific operation of this bulb, or should it work on all cars?
Thanks!