ah, Brasso ... savior and anathema both for everyone who ever joined the ranks ... basically, if you have a DD Form2, you both hate and love the stuff...
here's the deal: Brasso has ammonia in it, as well as some other stuff. now, your brass parts probably never had a 'finish' (i.e. a thin coat of clear paint) on them, as the insignia did. but Brasso take off the clear coat and leaves the raw brass, which looks shinier for a good twenty minutes to half hour, after which time the brass does what brass does.
so, if you insist that your brass be super shiny for a short period, then take Brasso and do your thing. other than that, well, not so much.
if you are keen to have your brass shiny on a longer term basis, you might try to clean it up and then apply Rennaissance Wax (or a similar product). Renn Wax is a bit on the pricey side, but a little bit goes a very long way.
I'm a fan of iron, so I don't have much brass going, and what I do, well, let's just say that the Sergeant Major would not be very impressed...
make good smoke!