To find the serial killer, you will have to head to three specific locations where a murder took place. In the same location, you will find a piece of a map. Once all have been gathered, you will be able to get to the serial killer.
There's also no time limit to find the serial killer and unlock the American Dreams Stranger mission. Everything can be done as soon as you are able to explore the map freely at the beginning of Chapter 2, and you can hold off in completing this Easter Egg even until the Epilogue.
Full Video Guide
Murder Scene 1
The first murder scene can be accessed very early in the game, as it's close to the Valentine area. The precise location is found to the south of Wallace Station, right below the "T" in Station on the map and right past the river.
Once at the area, search for a rock with the remains of a person. To the left of the mutilated body is the corpse's head. The map is inside the head.
Murder Scene 2
The second murder scene can also be reached pretty early in the story, as it very close to the town of Valentine, which is the main stage of most of the Chapter 2 Story Missions. The murder scene is located to the south of Valentine, to the west of Citadel Rock, below a bridge.
This time, the serial killer decided to hang its victim's body and sever its head once again. The head is located nearby, check it out to find the second map revealing the madman's location.
Murder Scene 3
The third and final murder scene can be accessed easily during Chapter 3, as it's located near Braithwaite Manor, a location players need to get to multiple times during the duration of the story chapter. The body of the last victim can be found under a tree east of the manor, right on the S of "Meadows" on the map.
The body is hanging like the second one, but you will need to head to the back of the tree to find the head with the third, and final, map piece.
Putting the Map together
Once all three pieces of the map have been gathered, take a look at it by accessing your Satchel through the right direction button on your controller. The map shows a burned down house. Flip the map to read the killer's challenge. Once all this has been done, a Stranger marker will appear on the map. Accessing it will begin the American Dreams Stranger mission.
The Stranger marker on the map is located to the southwest of Valentine. Head over to the highlighted area on the map and search the area for a burned out hut, which is the same as the one depicted on the map.
Nearby, you will find a hatch. Open it and get inside the cellar to find two different letters on the table. The letters, which have been written by the serial killer's mother, reveal some information about the madman, including his name, Edmund.
You are still not done with the cellar. On the contrary, the best is yet to come. Equip the Lantern and look around the cellar to discover yet another mutilated body. Get close to it to be assaulted by Edmund himself. You will now have to fight the madman in a melee fight.
As he is armed with a knife, he can deal some real damage to Arthur, so always keep your guard up, avoid his slashes and punch him when you notice an opening. Once you have damaged your enemy enough, he will get knocked out. Hogtie him and bring him to justice.
Once you have put the killer on your horse, head over to the Valentine sheriff office. Here, Arthur learns that the killer's full name is Edmund Lowry Jr. and that he never knows when to surrender, as he will try to bite the sheriff as he is about to be put in a cell. Shoot the madman to save the Sheriff, and if you're not feeling particularly confident, you can use Dead Eye to get a well-placed headshot.
Once Edmund is dead, the sheriff will thank Arthur for the help and reward him with around $20. The total amount slightly varied depending on Arthur's current Honor rating. Once the sheriff hands Arthur the reward, the American Dreams Stranger Mission is complete.