Hand signals is all that are required in most states on a moped. I dont disagree with the added safety of a functional and bright brake light. Just is another thing to go wrong on a bike and if you assume it hasn't burnt out then you are asking for trouble too, as your story illustrates. Sometimes a burnt out brake light will even prevent the bike from running.
Mopeds are dangerous no matter how you shake it. Ride safe, be alert.
Check the moped wiki for an exact wiring diagram for your bike.