What is gun extractor rod?

Answer 1

No such thing. There is, however, a gun ejector rod that is used on revolvers to eject spent brass.

You may also be thinking of a "shot extractor" for cannons, which was particularly common in the age of muzzle loading weapons. This was a long pole (or rod), typically with some sort of hook, basket, or twisted wire "worm" on the end. This was inserted into a cannon which had been fully loaded, from the muzzle end. It would be used to first remove the tamping wad (the bit of cloth used to keep the shot and propellant in), then the shot, then scoop out the propellant.

There are similar things on large breechloading cannons (typically, those found on naval vessels), most from the age of the the steam battleship (late 1800s to mid-1950s). While the breech could be opened, something was still needed to pull out the propellant charges and the round itself, and many gun turrets were equipped with a hydraulic extractor to do this (as the shell and propellants weighed far too much for it to be done by hand).