Just for the hell of it, I bought some steel wool and started to polish the tea kettle I got several months ago. I set my price pretty high, and it hasn’t sold.
I switched my game to using toothpaste to get a better polish. Here are the results so far.
Polished with steel wool. 
Polished with toothpaste.
I have some other polishing compounds, so I’ll try those as well.
I don’t generally associate Showa retro vintage Japanese alumi tea kettles with shiny finishes, but maybe it’ll sell. The patina on the pot, so far, hasn’t had the appeal that I thought it would.