@Quispieの回答に従いましたが、最初はWindows 10では機能しませんでしたが、それを解決するための基盤とソース（賞賛）とhttp://www.pinvoke.net/を提供してくれました。
[DllImport("user32.dll", CharSet = CharSet.Auto)]
public static extern IntPtr FindWindow(string strClassName, string strWindowName);
[DllImport("shell32.dll")]
public static extern UInt32 SHAppBarMessage(UInt32 dwMessage, ref APPBARDATA pData);
public enum AppBarMessages
{
New = 0x00,
Remove = 0x01,
QueryPos = 0x02,
SetPos = 0x03,
GetState = 0x04,
GetTaskBarPos = 0x05,
Activate = 0x06,
GetAutoHideBar = 0x07,
SetAutoHideBar = 0x08,
WindowPosChanged = 0x09,
SetState = 0x0a
}
[StructLayout(LayoutKind.Sequential)]
public struct APPBARDATA
{
public int cbSize; // initialize this field using: Marshal.SizeOf(typeof(APPBARDATA));
public IntPtr hWnd;
public uint uCallbackMessage;
public uint uEdge;
public RECT rc;
public int lParam;
}
[StructLayout(LayoutKind.Sequential)]
public struct RECT
{
public int Left, Top, Right, Bottom;
public RECT(int left, int top, int right, int bottom)
{
Left = left;
Top = top;
Right = right;
Bottom = bottom;
}
public RECT(System.Drawing.Rectangle r) : this(r.Left, r.Top, r.Right, r.Bottom) { }
public int X
{
get { return Left; }
set { Right -= (Left - value); Left = value; }
}
public int Y
{
get { return Top; }
set { Bottom -= (Top - value); Top = value; }
}
public int Height
{
get { return Bottom - Top; }
set { Bottom = value + Top; }
}
public int Width
{
get { return Right - Left; }
set { Right = value + Left; }
}
public System.Drawing.Point Location
{
get { return new System.Drawing.Point(Left, Top); }
set { X = value.X; Y = value.Y; }
}
public System.Drawing.Size Size
{
get { return new System.Drawing.Size(Width, Height); }
set { Width = value.Width; Height = value.Height; }
}
public static implicit operator System.Drawing.Rectangle(RECT r)
{
return new System.Drawing.Rectangle(r.Left, r.Top, r.Width, r.Height);
}
public static implicit operator RECT(System.Drawing.Rectangle r)
{
return new RECT(r);
}
public static bool operator ==(RECT r1, RECT r2)
{
return r1.Equals(r2);
}
public static bool operator !=(RECT r1, RECT r2)
{
return !r1.Equals(r2);
}
public bool Equals(RECT r)
{
return r.Left == Left && r.Top == Top && r.Right == Right && r.Bottom == Bottom;
}
public override bool Equals(object obj)
{
if (obj is RECT)
return Equals((RECT)obj);
else if (obj is System.Drawing.Rectangle)
return Equals(new RECT((System.Drawing.Rectangle)obj));
return false;
}
public override int GetHashCode()
{
return ((System.Drawing.Rectangle)this).GetHashCode();
}
public override string ToString()
{
return string.Format(System.Globalization.CultureInfo.CurrentCulture, "{{Left={0},Top={1},Right={2},Bottom={3}}}", Left, Top, Right, Bottom);
}
}
public enum AppBarStates
{
AlwaysOnTop = 0x00,
AutoHide = 0x01
}
/// <summary>
/// Set the Taskbar State option
/// </summary>
/// <param name="option">AppBarState to activate</param>
public void SetTaskbarState(AppBarStates option)
{
APPBARDATA msgData = new APPBARDATA();
msgData.cbSize = Marshal.SizeOf(msgData);
msgData.hWnd = FindWindow("System_TrayWnd", null);
msgData.lParam = (int)option;
SHAppBarMessage((UInt32)AppBarMessages.SetState, ref msgData);
}
/// <summary>
/// Gets the current Taskbar state
/// </summary>
/// <returns>current Taskbar state</returns>
public AppBarStates GetTaskbarState()
{
APPBARDATA msgData = new APPBARDATA();
msgData.cbSize = Marshal.SizeOf(msgData);
msgData.hWnd = FindWindow("System_TrayWnd", null);
return (AppBarStates)SHAppBarMessage((UInt32)AppBarMessages.GetState, ref msgData);
}