When I first bought my bike (used) in 2000 it had a YZ fender and one of those mounts you're writing about. The previous owner put on one of those plastic fender braces to keep the fender from flexing. It didn't work. I tore off the license plate several times when it connected with the tire knobs. I eventually got a WR fender which is much stiffer and more resistant to flexing.
Here's how I mounted the license plate on the WR fender:
The license plate light is a 5 mm white LED that is connected in with the taillight circuit.