What determines this?

[harperfan7]

Spoilers ahead

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If you handle the faceless at foundry before rail crossing, you have a special dialogue option with the mindreader at buzzers.  One person on the discord went the Hugo route, but the mindreader still wouldn't accept his plea to spare buzzer.  Another person did the same thing and the mindreader accepted it and spared buzzer.  Neither player had persuasion.  I tried it, and it worked for me; I did have persuasion but never chose a persuasion option in the dialogue.  The first player went and got the bloody mobile computer to see if that made a difference; it didn't. 

What determines if this succeeds or fails?

[PhrygianDominant]

For future reference: The Faceless telling you about their investigation (npc_fofaceless_toldAboutInvestigation  = true) leads to a different branch after the mindreading. If you haven't finished their quest (quest_fo_facelessRecon_finished = false), you are offered the persuasion option. If you have, then you get a line that should always pass and has no additional conditions. So basically, if you finish the quest you shouldn't need persuasion at all.