The quickest way of testing is to see if you have a EARTH at the IND terminal, this is the one onto which the blue wire to the warning light goes, when engine is stopped tis will be earth at this terminal, and will change to LIVE once running to show charging and so extinguish the bulb/light.
The part of the alternator that is affected is the regulator/rectifier, but not too expensive, around £45 should do a new recon ok.
tabetha