The fact that restorers are able to improve the shine show that they are not anodized. Even mothers mag polish would have no effect on anodized aluminum other than cleaning off dirt. Generally, if your rag turns black, you're polishing bare aluminum.
I cut the stiff bristles of a small paint brush down to about 1/4" and use that to scrub the grooved areas. It can serve to polish by adding a bit of mothers and working it in as well as a finishing step to lift out remaining black compound.
Bruce
