The radio station is surely the infamous Dr. John R. Brinkley's border blaster XERA-AM (formerly XER-AM), which broadcast out of Del Rio in Villa Acuña, Coahuila, throughout the 1930s. The Del Rio station became known as Hillbilly Hollywood, helping to launch the careers of a number of country artists (including Patsy Montana, Jimmie Rodgers, Red Foley, The Carter Family, and many others).
Brinkey's main purpose in setting up the station, however, was to continue promoting his bizarre goat gland treatments which he posited as a cure for impotence. It was because of his earlier experiments in transplanting goat testes into men throughout the U.S. that Brinkley had originally been chased out of the country. The station was eventually closed by the Mexican government in 1939 following U.S. pressure. *
You can read more on Brinkley and the Mexican border blasters, as well as listen to an extract from one of his goat gland adverts, here.
Needless to say, the quality of music played on Brinkley's station was more reliable than the medical advice.
* Although McCarthy rarely provides specific dates in the novel, it does appear he has taken some liberties here. Having already referenced Hawbaker’s book from 1941, Brinkley’s station at Acuña shut down in late 1939 and broadcasting from the station did not resume until 1947 as XERF-AM.
Most of The Crossing’s other historical references add up if we take the years 1941 to 1945 as the period of the novel’s setting.