I thought these might have been ecu controlled charging circuits but doesn't sound it from your description.
Anyway the thin wire leading to the dash charge lights only needs a earth to illuminate the light, with ignition on, so check the wire isn't earthing out on something, the earth would normally come from the alternator, which changes to live upon charging hence putting the light out, so needs sorting asap, look for a worn through wire etc between alt and dash light.
tabetha