I usually attack it with a terrycloth and some Flitz. A little will go a surprisingly long way.
There are various methods of oiling, waxing, or otherwise preserving it afterwards. I prefer boiled linseed oil for that, personally.
In Ye Modern Times, you could also just make your mail out of something that doesn’t rust. I didn’t, though.
Thanks.
I have a set of matching super historically authentic pants in the same pattern and material (with suspenders!) as well. I might even still fit in them, but I haven’t tried in a while.