Extrude face down without disturbing adjacent surfaces I am new to Blender.

I am trying to make a neck for my character's head, by extruding a face on the underside of their head.

I am trying to achieve this:



But when I press e to extrude, or drag down with the transform tool (orientation set to Local), I get this:



So I set the transformation orientation to Global, and I get this:



My character head currently:



Could anyone please guide me in the correct direction?

Many thanks.
By default the extrusion will follow the face normal (it's orientation). If it's not vertical the extrusion won't be either. To extrude and constrain on the Z axis just press E then Z.

Also, for this kind of faces that stick to the mirror axis, if you enable the Mirror Clipping option it will prevent the creation of a face on the axis itself.