I would be looking for some major high resistances between the alternator and the battery, seems the alternator is having a hard time, unless the new one is duff ?
Even in the event that the ignition/charge warning light doesn't come on it is normal for the charge to start when revving to about 3K, BUT it should stay charging until it is next switched off, then upon restart 3K will get it charging again.
The bulb lights up by receiving a EARTH from the IND terminal on the alternator when the engine is NOT turning, starting the engine causes the alternator to start charging immediately, the IND terminal changes to LIVE, so putting the light out, as it needs a earth, but now has two lives.
tabetha