how can i tell if my alternator is faulty or my wiring?

4 days ago my battery light came on on the dash after about 15mins it went out again, on the way home from work it did the same again it is now on permanently the van starts ok and the battery still seems strong i put a multi meter on the battery and it measured about 12.5v i turned the lights on and it dropped to 12.25v and stayed at that and didnt drop any further. i pulled out the plug on the alternator started the engine and the light was out put the plug back in and the light came back on. any ideas??? my van is a vauxhall combo 1.7 diesel and is a 97 model