In his first storyline, mysterious collector and reclusive actress Olivia Vancroft wants Mark Shaw's Manhunter mask for her wall of masks. Vancroft hires the shapechanging assassin Dumas to get it for her, and hiring an assassin for a basic theft may not have been a great choice, since Dumas proves overzealous and goes after Shaw and his family. To protect them, Shaw offers Vancroft his mask, but she tells him that Dumas' code of honor won't let her cancel a job. Before he leaves, Vancroft asks Shaw to put on his mask, perhaps not realizing the sensors in it would reveal her secret...
Shaw returns later, as Manhunter, to blackmail Vancroft: she and Dumas are one in the same; Dumas being his male identity, and Vancroft his idealized woman. Unfortunately, Shaw forgot one important detail in his plan:
Shaw was already outmatched, but now on Dumas' home turf he doesn't have a chance. Dumas offers him the chance to kill himself, but Shaw declines, deciding to fight it out. He realizes the collection is Dumas' mask, and starts to destroy it, luring Dumas into the open for the kill:
I'm willing to bet Shaw picked the Peacemaker mask because it's a big, metal lump; and not for the irony. Dumas dies, and Shaw leaves both their masks in the collection: unlike a lot of masked heroes, Shaw has no particular attachment to his. It's just a mask. In a nice touch, he leaves his mask with three of DC's prior Manhunters'.
From Manhunter #4, "Through the Mask" Written by John Ostrander and Kim Yale, pencils by Doug Rice, inks by Kelley Jones.
Researching for another post, I realized on this and Peacemaker's other post, I started typing his name as Peacekeeper halfway through. No one appeared to notice, which should tell you all you need to know about him.