Thanks to OriginalGriff and Ralf Meier...
Their guidance led me to the solution pasted below.
But first, I need to clarify my originally posted scenario. It seems that the code line below
WILL work if there is no other form opened during the process, such as a Filedialog window for instance.
Cursor.Position = PointToScreen(Button1.Location)
But if another form will be opened during the process, even if it is before the Cursor.Position statement, the cursor position is not positioned properly to the button1 location within the groupbox.
There may be a simpler way to bring the orientation back from the opened window so that code line will work, but I haven't found it.
As a result, I worked out the following solution (Note: I am a hobbyist so there likely a more correct way to code this):
In the Class Statement the following was added:
Dim WaitCurPt As New Point(0, 0)
In the code where I wanted to set the cursor position, the below was added wherein the actual names of the desired Groupbox and Button are used (without any quotations around their Names):
Call WaitCursorPoint(GroupBox1, Button1)
Cursor.Position = PointToScreen(WaitCurPt)
Cursor = Cursors.WaitCursor
Application.DoEvents()
Finally, the following subroutine was added:
Private Sub WaitCursorPoint(ByVal grp As Object, ByVal Obj As Button)
Dim x, y As Integer
x = grp.Location.X
y = grp.Location.Y
x = x + Obj.Location.X
y = y + Obj.Location.Y
x = x + Obj.Size.Width / 2
y = y + Obj.Size.Height / 2
WaitCurPt.X = x
WaitCurPt.Y = y
End Sub