Never dull works great.
You can also use rubbing compound meant for paint work.
Start with coarse and work up to the finest grit compound.
Power tool ? Use felt polishing bobs at low speed. Use a separate buff or bob for each grit .
Do not mix them up.
Sneak up on the final finish.
If the oxidation is heavy?
Some aluminum parts I've cleaned initially with SOS pads.
Chemical cleaners like aluma-brite have to be used sparingly and parts immediately thoroughly rinsed in cold water blown dry, then lightly oiled to arrest any further oxidation before final polishing.
Step Away From The KOOL AID !