Here comes the Hints from (BigRedBass) Heloise, your remedies for crusty Alembic brass:
First off, forget the tailpiece: They are all clear-coated so you won't have to mess with them, and if your axe has any gold-plated parts (tuning keys or others) DO NOT use any of the following on plated parts !
For really discolored uncoated brass (say, the adjustable nut or the bridge, for instance) get thee to an auto parts store and find a product in a can caller Eagle One Never Dull wadding. Inside is a material like batt insulation that's coated with a solution that will take you to shiny brass RIGHT NOW. Once you're shiny, you'll have to wipe it several times with clean cloths to remove the residue. Then you're good. I never saw any interaction with the wood finish, but I'd keep it away from it as a precaution.
If it's slight, a good car wax will also take you back to shiny. I'd use a good straight wax (not a product marked wax polish, which contains micro compound to remove slight polish lines).
Either way, once it's back to shiny like a new coin, you can use a light coat of Alberto VO5, yes the men's hairdressing in the gold toothpaste tube. This is totally organic and harmless and will keep brass shiny for a LONG time.
For lubing the tiny screws like the adjustable nut or the traveling screws on the bridge, I use BreakFree CLP, one of the wonder gun lubes. Totally harmless to finish and electronics, just a drop on these screws will sweat-proof them for a long time.
I used these fixes on mine and they worked like gangbusters. For me, Flitz was about useless.