Main question
I have a 2010 VW Jetta. I live in New Jersey. I'm due for a safety inspection in eight months and have an airbag light that's on. As far as the dealership can tell, nothing is wrong with my airbag system, there is just a burned out or short in the wiring that keeps the light on. Will a lit airbag light cause me to fail safety inspection in New Jersey?
Details on the airbag light
Last summer, the airbag light turned on and I had the dealership look at it. They eventually determined there was some short in the electrical system in the floor below the driver's seat area. They fixed the short, but the airbag light remained on. They tested the entire airbag system and found all the right voltages, so they think the airbag system is just fine but that the short had burned out some wiring associated with the airbag light. They're fairly confident the airbag system will work fine but were not entirely sure if the burned out wiring associated with the airbag light would affect things in a way they couldn't predict.
They told me that the only way to fix the airbag light is to replace the entire instrument cluster, a ~$900 repair. I decided I could deal with an airbag light and decided to not replace the instrument cluster. In the 9 or 10 months since then, everything in the car has worked just fine except for the still on airbag light. I also had a different garage briefly check the airbag light when I was in for something else. They were confused when their machine didn't register any error codes when they plugged it in, so this seems to sustain the dealership's story.