In #3, I would capitalize "Manager" since it is the proper name of the position he resigned. If you turned it into an adjective, you wouldn't need to capitalize it: "He resigned his managerial position." Alternatively, you could use the noun as an adjective without capitalizing it: "He resigned his manager position."
#1 and #2 are acceptable but become more clear if you change the word order:
"He resigned after eight years as Manager (or 'as a manager').
I don't like #4 or #5 because these sentences don't say what he resigned from. He resigned while he was a manager - that is clear - but what did he resign from? I know that seems strange, but consider this example:
Jack, the manager, performed many jobs at the company. He was the person in charge of hiring. He was the person who instructed new employees. He kept the company's books. It was too much for him to do, so he resigned his position as instructor of new employees.