Rub down with Magic Erasers, or the lighter/wet paper towel method to remove the oxidation. Make a paste of water and Barkeeper's Friend, apply to stem and let dry. Thumb buff the Barkeeper's Friend off and rinse with water and dry. Apply a small dot of plain white toothpaste such as Colgate to your thumb and evenly coat the stem. Allow to dry a bit, 30+ minutes, and thumb buff until gone. The toothpaste may need 2-3 applications, but more often than not, one application suffices.
Do you get a sulfur smell when you rinse the stem?