My view is that a 10 year old battery , even Japanese, is pretty old. The oldest battery I have ever had in motoring since 1966 is 9 years for a Bosch.
So be prepared for a new one. Some items that drain a battery and are overlooked are the interior light being left on, the boot light being left on and the radio. Also the alarm sytem uses electricity.
The charging light will go out of the alternator is fine, and do the lights dim and brighten as the car is revved up?