Head to Goodsprings Source, and towards the water tub, you'll see Barton Thorn wandering around. Talk to him, and he'll plead for your help to save his girlfriend trapped by Geckos. He'll give you clear directions on where to go: head towards the broken radio tower, then turn right. There you should be going up an incline.
There will be broc flowers growing on the slope. As you go up, you should see a path forking off towards the right. There is a refrigerator, bed, and some loot (the optional cache). Be careful, however, of the three bear traps. This area is also a Wild Wasteland trigger area.
It is advised to kill all the Geckos on your way up. On your way down, Barton will be right there carrying a pistol, revealing his clever ruse and turning hostile. Kill him for some loot.
Notes
Barton Thorn isn't always dressed the way you can see on the picture. More often he wears a very simple clothes (see Barton Thorn page). The reason why this image was added is to show you that he may look different.
The prospector's camp can be reached without exiting the invisible boundary that finalizes character's attributes and skills by maneuvering southward along the clifftops from Victor's shack. This route is useful in reaching the camp while avoiding the Geckos guarding the ridge as well.
If you wish, you can kill Barton Thorn without karma penalty and don't go up in the hill, since this will trigger the "reset character" as it's considered that you are entering the Wasteland.
It is recommended to kill all the Geckos when going up. If some are left alive, they may attack later together with Thorn.
Sometimes Barton Thorn will not come up the slope behind you, but after waiting or sleeping he completes the quest.
After the truth is revealed by Barton, the Courier can flee instead of killing him. The Courier can then return afterward to find his unconscious body, which can easily be thrown off the edge of the nearby cliff!
Barton can be killed for the loot he carries. Following that, quick travel to Goodsprings and back to his corpse. His body should have respawned with different armor and weapon, which can then be looted from him.
Because of the Geckos spawning in the area, he can sometimes be found already dead before the player can talk to him.
Trivia
The title is a reference to the Coen Brothers movie Barton Fink.