Hey guys, new to the forum! My apology in advance if this not the right place to post my Comments and/or Question.
I am experiencing similar situation but for different reason. My was one more victim of catalytic convertor theft, as you know is very common nowadays.
Shortly after the Battery light when on, Stop by Auto Zone to test the Battery and diagnostic said battery is good but the Alternator is bad. I replace it a new DENSO unit, but the Battery light remain on. I find that Honda has an ELD (electronic load detector) mounted in the fuse box under the hood,
That anybody experience similar Problem? Any idea or suggestion?
Thank you.

 

Moved your post to a new thread to make things less confusing.

Do you have a volt meter to test battery voltage with the engine off and with the engine running?

 

Yes, I check the Battery and 12.4 Volt and the Alternator is 14.5 and check all the fuses and they are ok, Battery terminal are clean and tight. I will post a picture later.