Light not coming on with the key on but engine not running does mean that something was wrong.

 

wanted to give you all what I hope is my final update on this mystery. I replaced the alternator and now the battery light comes on when I turn the key and it has started the last 3 mornings without issue. I hope that this helps someone else who is wondering why their battery is being drained overnight.

I noticed that alternators seems to last roughly 7 yrs and then start to quit and break down. I will make note of this in my calendar so that in 7 yrs I'll be expecting this.