The reg/rec probably failed because of not using a battery and could have a direct short.
A battery isn't just there to start the engine or for the lights to work without it running, it's there to balance the load on the system. Without it, the reg/rec is having to deal with it all and shunt everything to ground. They tend to get excessively hot when doing that.
Typically, when one part or another goes bad in a charging system and continues to be operated without repair, it takes the other out with it. Bad batteries take out alternators and bad alternators (when their reg/rec fails) take out good batteries.
Sounds like you'll just have to replace the reg/rec and if you don't want to use a battery, you'll at least want to use a large capacitor. It used to be called a battery delete back when enduro riders started using capacitors in lieu of a battery, to save weight and have a more durable system for hard off-road racing.
You could always look into using a super capacitor instead of a battery. It won't save any money over a battery, but it won't go bad sitting there for months on end either, although it will loose charge.
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