How do you change whether an NPC trainer within a faction offers services to those outside or inside the faction? I'm thinking about making a mod that allows more Telvanni NPCs to offer training to non-members once the Mages Guild Monopoly quest is completed, but have no idea how to change/affect this flag. Thanks!

Is not the Mages Guild monopoly an exclusive Telvanni quest? My point being that the player would have to be of House Telvanni for it to be offered and therefore would be eligible for training regardless of the status of the quest? In case I am mistaken and there are ways for this issue to be raised for non-Telvanni players, this is the approach I would suggest:

Create a 'Service Refusal' entry (under the Persuasion tab) filtered for the NPC's ID, or if you are creating several new NPCs you could add a script that declares a unique local variable that you can use as a filter and create a single entry that all of your trainers will use. Add filters for [Function: Same Faction = 0] and [Journal: HT_Monopoly != 100] (not equal to 100). So long as the player is not Telvanni and the quest has not been satisfactorily completed the service refusal text will display. If either one ceases to be true training will be offered.

Nice attention to detail, by the way.

Edit: inevitable typo.

Edit: sorry, serious blunder fixed.