The alternator on my '03 XLS failed instantly. Was working 100%, then not at all. Believe me, you'll know it when it fails. /QUOTE]
Alternators USUALLY fail more gradually, and in my experience with them, most often their output falls, due to worn brushes which beging to make "iffy" contact with the "slip rings", thereby reducing the unit's output capability.
The dimming of lights when more and more electrical load is added (blower, a/c/, etc.) strongly points to that type of condition. But, semantics, the alternator will need to be rebuilt/replaced either way. If voltmeter check shows battery voltage over say, 13 volts when running, with all electrical accessories off, at least the vehicle may be driven awhile without draining down the battery. If the alternator's output is zilch, or nearly so, the vehicle will be running on the battery alone, draining it to the point where it will not re-start the engine. imp