I don't have an F2 but I have found a ring once that was marked "10k & Sterling", it gave a very unusual signal and had a similar patina on the outside.
Cool ring for sure with the gold on the inside. What does it look like cleaned up? A little baking soda will tell you if the outside is silver or not. Nice find
XP Deus / Garrett AT Pro,Garrett 5x8, Nel Tornado / Garrett Ace 250
Garrett Pro Pinpointer/ Minelab X-terra 705 / Makro pinpointer / Nel Tornado coil / Nokta Fors Core