In a standard module of the VBA project, paste the following code:

Public RunWhen As Double
Public Const NUM_MINUTES = 10

Public Sub SaveAndClose()
    ThisWorkbook.Close savechanges:=True
End Sub

Change the value of NUM_MINUTES  to the number of minutes you want to leave the workbook unattended before closing.

In the ThisWorkbook module, paste the following code:

Private Sub Workbook_Open()
    On Error Resume Next
    Application.OnTime RunWhen, "SaveAndClose", , False
    On Error GoTo 0
    RunWhen = Now + TimeSerial(0, NUM_MINUTES, 0)
    Application.OnTime RunWhen, "SaveAndClose", , True
End Sub

Private Sub Workbook_BeforeClose(Cancel As Boolean)
    On Error Resume Next
    Application.OnTime RunWhen, "SaveAndClose", , False
    On Error GoTo 0
End Sub

Private Sub Workbook_SheetChange(ByVal Sh As Object, ByVal Target As Range)
    On Error Resume Next
    Application.OnTime RunWhen, "SaveAndClose", , False
    On Error GoTo 0
    RunWhen = Now + TimeSerial(0, NUM_MINUTES, 0)
    Application.OnTime RunWhen, "SaveAndClose", , True
End Sub

Private Sub Workbook_SheetSelectionChange(ByVal Sh As Object, _
    ByVal Target As Range)

    On Error Resume Next
    Application.OnTime RunWhen, "SaveAndClose", , False
    On Error GoTo 0
    RunWhen = Now + TimeSerial(0, NUM_MINUTES, 0)
    Application.OnTime RunWhen, "SaveAndClose", , True

End Sub
 

This code cancels and reinstates an OnTime event whenever a cell value is changed or when the selection is chagned. If neither changes in the specified amount of time, the workbook will save itself and close.