After researching methods to clean metal accordion grills without successfully finding an easy and not so risky approach (commonly discussed methods included having to remove the grill cloth then using a metal polish such as Brasso), a fellow accordionist recommended the Mayflower Metal Care Cloth which apparently can be used on your accordion’s grill without affecting the grill cloth underneath.
Eager to try something quickly, I found an alternative stocked in Australia, Cape Cod Fine Metal Polishing Cloth (contains petroleum distillate, whereas the Metal Care Cloth is non-toxic) available for around $13 AUD. I can only imagine the non-toxic alternative would be a better and safer solution, however the Fine Metal Polishing Cloth worked wonders. If choosing the Australian alternative, I highly recommend doing this in a highly ventilated area, such as an outside space.
For optimal results, I recommend polishing the grill twice, buffing in between each round with a soft, dry cloth. This process took all of 10 minutes, without the need to remove the grill cloth, and left me feeling as though my accordion was brand new.
Hopefully this can help anyone looking for an easy way to make their dulled accordion grill shiny again.