Thank you.
So lets say I play a Mox Sapphire and my opponent has a Gorilla Shaman in play. I have a Tinker in hand. Does my opponent get any priority in between me resolving Mox Sapphire and me wanting to play Tinker?
Not unless you (unwisely) choose to pass priority first, after Sapphire resolves, the stack is empty and you have priority to play sorcery speed spells.
Just to be clear, this is assuming you played the Mox Sapphire during your turn (i.e. you didn't play it during your opponent's turn with Vedalken Orrery or some such shenanigans).
115.3b The active player receives priority after a spell or ability (other than a mana ability) resolves.