Try this variation.

Private Sub Worksheet_BeforeDoubleClick(ByVal Target As Range, Cancel As Boolean)
If Target.Columns.Count = 1 And WorksheetFunction.IsOdd(Target.Column) = True Then
    

    If Columns(Target.Column + 1).Hidden = True Then
        Columns(Target.Column + 1).Hidden = False
        For N = 1 To ActiveSheet.DrawingObjects.Count
            If ActiveSheet.DrawingObjects(N).TopLeftCell.Column = Target.Column + 1 Then
                ActiveSheet.DrawingObjects(N).Visible = True
            End If
        Next N
    Else
        Columns(Target.Column + 1).Hidden = True
        For N = 1 To ActiveSheet.DrawingObjects.Count
            If ActiveSheet.DrawingObjects(N).TopLeftCell.Column = Target.Column + 1 Then
                ActiveSheet.DrawingObjects(N).Visible = False
            End If
        Next N
    End If
End If
End Sub