How did they realize the truth about Josh?

Question

Beware of major spoilers.

In Insidious Chapter 2, when the Grandmother and the three "Ghost Hunters" follow the lead from the past to find out what happened to Josh, they go to the old hospital and from there to the house of the old man (Parker Crane). That's when they realize that it has not been Elise who spoke through the dice to them, but Crane's insane mother (mater mortis). They also realize that Crane was the bride in black, a crazy murderer who killed many people in his lifetime and also the ghost appearing on Josh's old photographs.

At that moment they decide to go back to the family house, get Josh's wife and the kids out and try to sedate Josh, apparently because they now know that Josh is not really Josh, but Crane who took his body.

How did they make that connection from the visit to Crane's old house?

Answer 1

Carl has a psychic vision of the black bride when he touches Crane's black veil, after which he says the following to Lorraine (Josh's mother):

Carl: Parker wore that dress to commit his murders. It was his disguise. He killed for his mother because she forced him to. He wanted his childhood back. That's why he went after your son.

Theses insights, along with the knowledge that Josh is currently possessed by Crane, are apparently gained from that vision along with applied deductive reasoning.