2 part question:
Wife moved out of house over 6 years ago. Has not been back nor attempted to get any personal belongings from the house. Does this qualify for Abandonment in getting a divorce?
Both have filed and signed at separate times, papers are at court house. How long does husband after to wait before getting a petition for the divorce to proceed?

Since most states now have no-fault divorce laws, the abandonment grounds are probably moot.If the papers have been approved by the court but unsigned by the other party within 6 months I would go back to the court and apply for a default judgment.