Joseph was last seen walking to his grandmother's house on Elmwood Court in El Paso, Texas, on September 9, 1974. Joseph's mother was washing the family's car in their driveway at the time, and his father was indoors. Joseph kept going from one parent to the other. When he disappeared, at first both his parents thought he was with the other. He has never been seen again. All of his neighbors and his parents, who are now divorced, were ruled out as suspects in his case, and a search of the Rio Grande, which flows behind his house, turned up no clues.

A neighbor reported seeing an unidentified blue Ford on the street, which dead-ends, at the time Joseph was last seen. The vehicle disappeared at the same time Joseph did, but it hasn't been proven that the car is connected to his presumed abduction.

Authorities believe Joseph is dead and they have a suspect, whom they have not publicly named, in his kidnapping and presumed murder. They presented their case to a grand jury, but the jury didn't issue any indictments. Police stated the passage of time since Joseph's disappearance has greatly hindered the investigation. The case remains active but unsolved.