If this guy can do it, I don't see why you can't.

http://www.miata.net/garage/swingplate.html

 

It looks to me that the thing won't flip back to the "viewable" position after you've stopped the car again. What makes it flip back?

 

I honestly have no idea, as I couldn't figure it out either. But with our S's, we could hang the plate under the top of the nose, so gravity would pull it down when you stopped. Not sure why the guy mounted it on the bottom of the nose.