Is this what you wanted? I basically just followed the instructions in your question!
private void Button_Click(Object sender, EventArgs e) {
Int32 index = 0;
clbx.SelectedIndex = index;
clbx.Focus();
Rectangle r = clbx.GetItemRectangle(clbx.SelectedIndex);
Point newPointerPosition = clbx.PointToScreen(r.Location);
newPointerPosition.Offset(r.Width / 2, r.Height / 2);
Cursor.Position = newPointerPosition;
}