I too wanted to just capture a mousemove event from a Listview during mousedown to enable this to execute a Form Move action. All other controls like PictureBox and Label etc return a Mousemove event so the user can click on any control and drag the Form around. But not Listview! Don't like overly complex solutions to fix a simple issue.
I found that setting the "Listview.Multiselect = False" did not fix the issue. But after much experimentation I had success with "Listview.FullRowSelect = True". Set This and voila... now the Mousemove event is captured by the Listview.