Clever idea- my arms have been permanently different shades since my 20's (I drive, so my left arm is darker). I don't think I would use this, though... It would collect dust just like the hoodie in your car did, and only serves one purpose. I use heavy sunscreen and always bring a long-sleeved shirt or light jacket. This way I'm ready to deal with the sun even when I finally get out of the car, not just when I'm driving.
I've also tried wearing just one sleeve of a light jacket, but found that my other arm (both sleeveless, and out of the sun) got cold. I suspect this would create the same problem.
Long story short, I think the market would be limited, but that certainly doesn't mean nonexistent. If I were you, I would consider putting the pattern up for sale on Craftsy. That way you don't have to invest in materials, production or shipping- just write up a digital pattern, and see how it goes!