"The hidden message here-don't overcomplicate this"
Hindsight is a wonderful thing. With all problems it is difficult to arrive at the final solution without going through all the possibilities based on the information to hand. In my experience, the only time a battery light has come on was when the alternator failed. You had a fairly recent alternator but it was proven to be faulty. We could have said- change the alternator- and the problem could have been the wiring. Glad you have solved your problem though.
If you think I've been able to help, just say