Select the range of cells to evaluate in the first column then run this macro:
Option Explicit

Sub CountVisibleMergedSectionsAddPageBreaks()
'Select the range of rows to evaluate in the first column then run this macro
Dim RNG As Range:   Set RNG = Selection
Dim MyRow As Long:  MyRow = 1
Dim BrCount As Long

    Do
        If RNG.Cells(MyRow).EntireRow.Hidden = False Then
            MyRow = MyRow + RNG.Cells(MyRow).MergeArea.Rows.Count
            If MyRow > RNG.Rows.Count Then Exit Do
            BrCount = BrCount + 1

            If BrCount = 13 Then
                ActiveWindow.SelectedSheets.HPageBreaks.Add _
                    Before:=RNG.Cells(MyRow)
                BrCount = 0
            End If
        Else
            MyRow = MyRow + RNG.Cells(MyRow).MergeArea.Rows.Count
        End If
    Loop

Set RNG = Nothing
End Sub