AOA;
I don't know about error codes, i am having code 13 too. Please guide me if you know about code 13.
A only blink when seat belt is off. While driving it must be Visible always(A sign appears and stays when battery charge reaches optimal level not immediately after driving ).
I think your battery is small for eco idle to operate. I am using DL48 Daewoo Dry battery which is equivalent to 65 local battries. as your battery is new, just try to borrow another big battery just for checkup.
If eco idle works then go for big size battery.