This is something that is very popular with the Miata crowd with their older cars. The raised lettering on the taillights and sidelight markers is a catchall for dirt and wax. It is a pain to keep clean with a toothbrush. The solution is to sand off the lettering starting at 400 grit and moving up to 1000/1500 grit and then finally polish with a dremel and plastic polishing paste or a wheel and paint polishing compound.
You can remove the lights to do this or just tape over the surrounding painted areas with painters tape to protect the surfaces.
Go slow with polish and keep surface wet otherwise you'll get too hot and melt the plastic.
Here is a before.
After.
