During the fight, the "good" Spectre actually pops out of his own zombie-fied body, which the evil version tries to smash back inside, using the Stranger and Blue Devil as cudgels.
Eventually Zombie Spectre departs, and we learn the Stranger's true mission (always mysterious, that guy): Deadman, who is busy fighting a Zombie version of his own dead body outside the gates of the holy city, Nanda Parbat.
The Stranger gets close, and he and Zombie Deadman (possessed by the "real" Deadman) tussle:
...I like the nod to the various Phantom Stranger origins, as told in Secret Origins #10.
Eventually, due to their combined efforts, Zombie Deadman is rendered inert, and his body--a sacred item to the citizens of Nanda Parbat--is laid out, and guarded "for as long as it is required."
This part of their mission accomplished, Deadman and The Phantom Stranger depart: