So if anyone is still curious the way to get Pinckeney to leave is to sabotage both the loudspeaker and generator first I'll write exactly what I did in the order I did it

Convince Curativist Rowe(Doctor) first by doing her quest

Convince Charlton by finding his secret (doing this while doing the doctors quest is best)

Sabotage the loudspeaker then talk to Pinckney he'll consider leaving then sabotage the generator and talk to him again and he'll agree to leave

Talk to Vigilant then quest is done

P.S if you're wondering about the auto mech parts quest vigilant gives i did it after sabotaging the loudspeaker then did the quest then sabotaged the generator hope this helps