I'm going to hazard more possibly the latter. Maybe one diode.
Clearly the battery was accepting charge when you turned the accessories off. Preseumably then the alternator was not keeping everything running with the accessories on. Was the battery showing discharge when the lights were on?
That's not a definative. Rob's suggestion is also good. Check that alternator output wire at each connection, and the battery positive and ground while your at it.
crib sheet version of power flow:
Understanding Charging Systems with Ammeter:
