Is "Billy Pilgrim" a play on Scott Pilgrim, I wonder?
Clarifying/expanding on what fasoaga said: Billy Pilgrim is the protagonist of Kurt Vonnegut's
Slaughterhouse-Five. After traumatic experiences as a POW in WWII he becomes "unstuck in time", which means he experiences moments from his life in an arbitrary, non-chronological order which he has no control over.
Sel has referenced this phrase before: in "Infinity House" the narrator described how people trapped there become "unstuck in eternity". As for Maya, she became unstuck in time during Halloween, living through moments from her past as if they were happening in the present. With an event title referencing that, I hope it means she's going to start telling Sensei about Halloween, though I'm sure she'll leave the Ami part out (the story won't allow him to learn about her yet).
My first thought with "A Second Haunting" is that it refers to Sekai's ghost (especially since she's in one of the Maya previews), in which case a second haunting could be Sensei seeing another ghost. Maybe there will just be multiple Sekais again, but the (very unrealistic) ideal scenario is that the ghost of Maya Prime shows up to snarkily comment on his passivity and indecision since her death.