Here's a write-up of all the specters:

Library

When the library goes dark, peek through the bookshelf. This will trigger Amy (Amy is tagged as a 'spirit' in the code at this point).

Locker Rooms

When you first see the rose door, inspect it closely, this will cause a ghost to investigate you.

In the girl's locker room, search for feet under the stalls

Gymnasium

In the storage room when you pick up the flashlight.

In the girl's bathroom making noise in the stall.

As you exit the dark gymnasium (as long as you hear them it counts).

Classrooms

Grab the face piece from behind the mirror in the bathroom

Audio Visual closet, when you pick up the strange key

In the secret underground closet, after you pick up the floppy

Sewers

After you place the first face piece. Ghosts appear to investigate

(List credits to the developer(s). Thank you Crista)