“This may not apply to all alternators.”
Yes, it does apply to all alternators. If the dash “charge” light is burned out or not making adequate contact to be functioning properly, the alternator (any alternator) will not charge.
Technically, the dash light wire (labeled “D+” on top of the alternator) provides an initial electrical path for the alternator field coil to begin charging once the alternator starts spinning. If the light is defective, no field charge. The alternator internal magnets are not adequate to maintain charge on their own. They need the field winding operating to start or maintain the charging sequence.
Glad you found the culprit. Most people wouldn’t look there, especially if the light is out!
Those little 4W bulbs in those little brass sleeves are notorious for corroding over time and failing to work (the solder button on the bottom of the bulbs, and where the sleeve inserts into the gauge, too). If you swap an alternator and still no charge, first place to look is the dash bulb.