Walk behavior issues - neck and shoulders

You might also try using the Rig Checker to see if there are any issues with your puppet.  On the Rig panel with your puppet showing, click on the warning (!) icon in the lower left hand corner of the window to open the Rig Checker.

I am guessing you have an independent head? Could you show screen shots of the Head and Body layers? My guess is you have something like the Neck tag as a part of the Head layer. I think it works better on the Body layer. Screenshots showing where the Neck, Head, etc points are would help, as well as the yellow mesh outline shown for the Body ahd Head layers.