So you're saying just the tractor with nothing behind it will do that? Like if you were driving it down the gravel road and trying auto steer with just the tractor, no implement. 

Seems like wheel angle sensor or the harness for the sensor. Or the EH valve but the first ones are easier and cheaper to check. 

You shouldn't need to "mess with" or "tune" the steering settings at all. Almost every time I've seen someone messing with those they weren't aware of one of the actual problems and just trying to mask it with settings changes. 

But first, confirm the implement guidance is OFF and you're not hooked to anything and see how it steers. That will narrow down a lot of things