If the brass stopper rusted off of the overflow switch and fell down the overflow it is more likely that the stopper is stuck in the chamber between the tub shoe and the overflow assembly ABOVE the p trap. When you flip the switch to fill the tub, the brass stopper wedges itself into that space to stop the flow of water. try lubricating the inside of the overflow and try to retrieve the stopper by the control rod (hopefully it is still connected) You may also be able to grab the control rod with a pair of needle nose pliers or a small snake. one last trick, if you have taken the p trap off then fish a plumbing snake down the overflow until you see it appear at the p trap connection. tie a small rag to the end of the snake and pull it back up through the overflow. if you dont get stuck you will pull the stopper back out with the rag.