Not the bulb...
I'm not so sure about the bulb idea...
In posting some alternator/charging problems here, I heard that bulb idea more than once. In trying it out, I did the following:
1. Started the car. Noted that the lamp worked during starting. Once the car was started and idling, the lamp turned off.
2. With the car running and the ScanMaster set to read battery volts, pulled the lamp from the socket.
3. No difference AT ALL in voltage output... remained at a constant 14.0 volts.
Since the charging rate remained steady and was unaffected, there is must be more than a burnt out bulb to cause anyone problems. While a problem could possibly be related to the bulb circuit, the bulb itself does not seem to have anything to do with it in my experience/opinion. Now, it could be burnt out so that you cannot tell the charging circuit is having a problem! Check this during startup.. It should light up and tell you the bulb is OK.
I later replaced the alternator and it corrected my intermittent charging issues. Since you have done this and it didn't help, your original alternator is probably fine.
My recommendation is to check the sense wire and the connector that plugs into the alternator. If the car is started/runs without this plugged in or with a poor connection, the alternator will not charge the battery. Look for an open somewhere on this wire. Also check the terminal inside the connector and that it mates with the pin in the alternator. Everything must be clean and free of any corrosion. NOTE: if this is open/unplugged, the battery lamp will not light!
Double check the primary wire/cable running from the battery to the alternator. Maybe something managed to cut through it and isolated the alternator, however, I believe the lamp would light up in this case.
Hope this helps!