I tape the body and sidpepipe openings with a good quality masking tape.
Use the Locktite Alum brightener (15% phosphoric acid) 1st. Leave on for 10 min and rinse. The pipes will be very bright and zero yellow.
Aluminum Jelly, Aluminum Polish, Aluminum Brightener, Aluminum Cleaner Directions from Loctite Adhesives
Then use a Rouge type emery stick with various mandrels.
The pastes have a ton of sling and are great for shooting rooster tails across the garage and and you vs actually staying on the wheel.
A good starter kit is sold thru Eastwood.
Stainless Steel Polishing Kit 14 pc Set