Joshua Henry never understood why his father owned “Time of the Last Persecution,” an obscure 1971 psychedelic-folk album by the British songwriter Bill Fay.

Henry, a 40-year-old songwriter and producer devoted to old-school analog technology, grew up in the woods at the edge of California’s Sierra Nevada. His father, Jamie, wasn’t a record collector: He reluctantly served in Vietnam before becoming an antiwar activist, then spent his final four decades as a hardscrabble logger. “Last Persecution” was never issued in the United States, and barely caused a blip in England’s very crowded singer-songwriter scene of the early ’70s. After its release, Fay vanished from music.

All his life, Henry remained curious about the Fay LP, with a portrait of a disheveled singer on its stark black cover. When he was caring for his father, who was battling cancer, the album became a lifeline between the two men. They’d listen to Fay, dissecting his peculiar mix of apocalyptic vision and hopeful grit. After his father’s death in the summer of 2010, Henry began trying to make good on a fantasy they had shared: to find Fay and help him make his first record since 1971.

On Friday, Fay will release “Countless Branches,” his third album in the 10 years since Henry tracked him down and urged him to return to the studio. Fay — now 76 and married, almost all he’ll allow about his personal life — has made as many studio albums this decade as in the previous six combined. Like the once-lost rock star Rodriguez or Fay’s fellow British folk singer Vashti Bunyan, he has been given an unlikely second chance in the new century. No one seems more puzzled about that resurgence, or leery of its potential spotlight, than Fay himself.