Is it actually charging, oddly enough it still can even with batt light on with certain faults.
Check the charge rate before engine is running and after, revving to around 3000rpm will start it charging so long as alternator is not buggered, whether the charge light works or not, this is the first thing to establish, next with engine stopped remove thin blue wire and the charge light should go out, the IND terminal it goes to on the alternator supplies a earth whilst the engine is stopped, but once running this changes to live so extinguishing the bulb, as two lives don't make light.
If you then with the engine running touch a LIVE onto the IND terminal it should initiate the charge process, if it doesn't the alt is buggered.
tabetha