The answer to the question “When do I need the ;; within OCaml source code?” is never.

     It's not a part of the language and is only used by the interpreter as an end of input mark. 

     Historical note: In CAML Light, the predecessor of OCaml, double semicolons were mandatory. For this reason they are quite common in old code originally written in CAML Light or written in the early days of OCaml. These days they are considered a bad style.