From my point of view, the strain hardening expont no influence on the neck position, only in how much the deformation extends from the area of thinning or fracture.
It is a good question, in my opinion, the position of the neck will depend on the triaxial stresses involved, therefore, the deformation is no longer evenly concentrated in the sheet metal, it will be concentrated in the weakest area and precisely at this point it is where everything is relevant, the surface of your sample to see if it has any stress concentrator or microstructure level if it has inclusions, see the limit of small-angle grain, precipitates or porosities, because due to these defects and triaxial efforts it is the place where the neck will be and you must find the point of instability for a more accurate analysis (the reason is obvious).
Now, having this clear we can analyze in more detail the effect of hardening by deformation in the position of the neck, this hardening is related to the movement of the planes in the deformation process and therefore, dislocations increasing their density and making it difficult for the plastic flow continues, this produces a compensation effect and generates a certain displacement in the neck area until they are compensated and the plastic flow associated with the deformation begins to flow again. Other additional considerations should also be taken, but that does not initially affect, as is the case with the associated temperature unless the conditions establish that they are relevant.
I feel it difficult to answer this thread. I don't think that strain hardening exponent affects the necking position of the sheet during the forming process. The thinning of the sheet takes place at the weakest point.