Depends on the case…Is it wood? I use Howard’s Feed & Wax put on per instructions by hand. Is is Brass? Use Brasso or Simichrome per instructions by hand…If lacquered brass Hm…Using polish will remove the lacquer…Is it Adamantine? This is a plastic veneer used by Seth Thomas and ?? I have used Flitz by hand (LOTSA Elbow Grease as this case was dull) per instructions..Is it pot metal?..I have seen wax used on them…By hand…Never really used power tools to polish a case…Unless it was a pocket watch case like silverode, or nickle…
Just my thoughts…
Jim