Using conditional formatting or VBA to automatically open the next drop down menu after selecting ?

Trismos 

If you want this functionality on each sheet of the workbook, you don't need to place the change event and selection change event codes on sheet modules of each sheet.

For that case, place the following codes on ThisWorkbook Module and to do so, follow these steps...

1. First delete the any existing codes from sheet modules.
2. On VB Editor window, double click ThisWorkbook in the project explorer pane, you will find it on left side of the VB Editor and paste the code given below into the opened code window.

In the attached, I have placed the codes on ThisWorkbook Module and created some duplicate sheets. So now the code works for all the sheets in the workbook.

Code on ThisWorkbook Module:

Private Sub Workbook_SheetChange(ByVal Sh As Object, ByVal Target As Range)
Dim n As Variant

On Error Resume Next
n = Target.Validation.Type
On Error GoTo 0

If n = 3 Then
    n = 0
    On Error Resume Next
    n = Target.Offset(1, 0).Validation.Type
    On Error GoTo 0
    If n = 3 Then
        Target.Offset(1, 0).Select
        SendKeys "%{Down}"
        SendKeys "{NUMLOCK}", True
    End If
End If
End Sub

Private Sub Workbook_SheetSelectionChange(ByVal Sh As Object, ByVal Target As Range)
SendKeys "{NUMLOCK}", True
End Sub