It helps to understand the basic setup for the alternator. ASD relay closes and sends battery voltage to the field winding in the alternator (post 90 and pre 98 I think/maybe later) The amount of current through the field winding is regulated by the PCM (ECM, computer) on the ground side. Don't know for sure, but it's likely it is regulated by the amount of voltage supplied to the PCM and not the output of the alternator. If the ASD relay isn't working the Jeep won't usually start or run.
The alternator has three diodes in there, each responsible for about a third of the output voltage (not exactly, but near enough).
80 amp fuse in the PDC (power distribution center, under hood fuse/relay box).
The alternator does have brushes and these can become worn or dirty, iffy or no contact will affect output.
Arching or loose power connections to the PCM, has been known to pulse and scramble the brains for the voltage regulator (TSB). In other words, unhook the battery before attempting to remove the PCM power plugs and try to avoid jiggling anything electrical, from the batter terminals, through the ignition switch to the PCM whenever possible. Sometimes the voltage regulator (driver) built into the PCM, just takes a dump.