So I solved this problem in my solution, although I'm not sure it will be cross applicable. Sadly, mine is in VB.Net, so there may need to be some translation.
First, I ended up not using ApplicationEvents4_Event Instead there are other built in event triggers you can use via "ThisAddIn"
Private Sub Application_NewDocument(ByVal Doc As Word.Document) Handles Application.NewDocument
'MsgBox("I opened something")
myCustomTaskPane = Me.CustomTaskPanes.Add(New MyCustomTaskPaneClass, "TaskPane", Doc.ActiveWindow)
myCustomTaskPane.Visible = True
End Sub
Using this method I did have a similar challenge. Running winword.exe, and thereby opening a new word document, did not trigger the NewDocument event. Luckily, there was another event to use - Document change.
Private Sub Application_DocumentChange() Handles Application.DocumentChange
'function to test if the ActiveDocument has a taskpane from my add-in, and then a function to add one
If Not HasMyCustomTaskPane() then AddCustomTaskPane()
End Sub
So - bottom line, regardless of if you keep using ApplicationEvents4_Event you should see if you can use the DocumentChange event. It triggers when a new word window is selected.