95% of the time problems like this are related to a fault in the rudder
feedback also known as the rudder followup. It is the device down below that is mechanically linked to the rudder stock. With these older units the whole device consists usually of a simple potentiometer.
I would first measure the voltage being sent to it to make sure it's correct. If it is then I would cut power and measure the resistance from hard over to hard over and see if the transition is smooth on the multimeter. If it isn't, if it look "jumpy", that would mean that the pot has a "dead spot" and would need to be replaced. You may not be able to replace the whole feedback, but you may be able to just replace the potentiometer.
Of course that all depends on if this particular AP uses a pot to begin with. I am not familiar with wagner but most older units use a simple pot although some older ones, some simrad
, use frequency signal instead of voltage.