Dead Cousin Ted can be found at the following locations for each character:Bernard
(kid with glasses in the present
): Just outside the main lobby as you start the game. Open the door and go outside to see Ted holding a birdbath.
(portly kid with the backwards cap in colonial times
): Just as you walk into the main lobby of the Inn, Ted is behind the counter wearing a tri-corner hat.Laverne
(kid with the crazy eye in the future
): After you get the costume and put it on, Ted is on the second floor in the middle room (In colonial times, this is Betsy Ross' room. In the present, it's the suicidal inventor's room
Once you encounter Ted with each character, be sure to speak with him. I went through all of the dialogue options to be safe. After the last kid talks to him, you should get the achievement.
If you see a way to improve this guide or want further clarification, leave a comment! Thanks!