TL;DR: Frank Rudolph Young was born April 16, 1911, in Panama City, Panama, and probably died June 24, 2002 at age 91, probably in Chicago, Illinois. His father was John A. Young and his uncle was Dr. Donald R. Young, a dentist. Frank married Gabrielle Reckinger in 1940.
The rest of this answer supports the biographical details with standard genealogical sources: census, birth/marriage/death records, immigration records, military registration, etc.
Frank immigrated to the United States under the name Frank Rodolf Young on September 10, 1928, on the ship "Santa Teresa" from Panama (Cristobal, Canal Zone) to New York City, arriving on September 17.
When he sailed, he gave his occupation as student at "University of New York" and his nearest relative as father John A. Young, Box 304, Ancon, C.Z. (Canal Zone).
The 1930 census shows Franco R. Young, 18, as born in Panama as were both of his parents. In this census, he is lodging in Chicago with a family named Weiss.
When he declared his intention to naturalize in early 1937, he gave his nationality as British and his race as Scotch-English. He was described as a dark-complected white male, 6 feet tall, weighing 170 pounds, with black hair and dark brown eyes. He was single at the time.
On another trip in 1937, he listed his nearest relative as Dr. Donald R. Young, Box 304, Ancon, Canal Zone.
In 1937 he was living in Los Angeles and gave his occupation as writer, but in 1940 he was living in Chicago and gave his occupation as laborer.
In October of 1940 when he registered for the draft he listed a wife Mrs. Gabrielle Young as his next of kin.
The Cook County, Illinois Marriage Index shows a Frank R. Young married a Gabrielle Reckinger on September 30, 1940.
Frank was finally naturalized in 1941.
The Social Security Death Index has a record for a Frank R. Young, born April 16, 1911, last residence Chicago, Illinois, who died on June 24, 2002 at the age of 91.
The SSDI has a record for Gabrielle Young, born Feb 15, 1909, last residence Chicago, Illinois, who died in November 1984.
I have not yet found an obituary for Frank/Franco Rudolph/Rodolf Young or Gabrielle Young.
Note that there were two Frank Rudolph Youngs in Chicago in the 1940s. The other one was born August 10, 1894, in Winnipeg, Manitoba, and registered for the draft in 1942. He married Gladys F. Johnson nee Thompson in Dubuque, Iowa, on September 23, 1940, a week before the other Frank Rudolph Young got married.
In his book, Yoga Secrets for Extraordinary Health and Long Life, author Frank Rudolph Young mentions Panama and an uncle who was a dentist:
A group of American doctors with Indians in the Panama Canal Zone declared that chewing sugar-cane was fine for the health. The doctors discovered, furthermore, that the cane fibers "clean out food from between the teeth." One of the doctors had even tried it himself.
My prominent dentist uncle in Panama learned this secret from these Indians about 80 years ago. . . . My uncle used it even after studying dentistry in the United States.
Compare the photo of the author in his 60s in 1971's The Secret of Spirit-thought Magic with the photo of Frank Rudolph Young from his naturalization paperwork.
About his uncle Donald:
In 1917, a Donaldo R. Young, born in 1893 in Panama, registered for the draft as a "dentist student" at Northwestern University.
In 1918, Donald R. Young married Rose Weiss in Cook County, Illinois. This is the county that Chicago is in; Weiss was also the name of the family that Franco R. Young was lodging with in 1930.
In 1945, a Dr. Donald Young, age 56, Panamanian citizen, flew from Merida, Mexico, to New Orleans, and his address is given as 3933-34 Pine Grove Av., Chicago, Illinois. Also on the same flight was U.S. citizen Rose Marie Young, age 45, with address given as 3933-35 Pine Grove Av., Chicago, Illinois. "Weiss" is written next to Rose Marie's name.
According to Donald's intake form, he was a dentist and was headed to Chicago to reside with his daughter Dorothy Young.
Ancestry.com. Illinois, U.S., Federal Naturalization Records, 1856-1991 [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2016.
Original data: Naturalization Records. National Archives at Chicago, Chicago, Illinois.
Ancestry.com. U.S., World War II Draft Cards Young Men, 1940-1947 [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2011.
Original data: National Archives at St. Louis; St. Louis, Missouri; WWII Draft Registration Cards for Illinois, 10/16/1940-03/31/1947; Record Group: Records of the Selective Service System, 147; Box: 2012
Ancestry.com. New York, U.S., Arriving Passenger and Crew Lists (including Castle Garden and Ellis Island), 1820-1957 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.
Original data: Passenger Lists of Vessels Arriving at New York, New York, 1820-1897. Microfilm Publication M237, 675 rolls. NAI: 6256867.
Ancestry.com. California, U.S., Arriving Passenger and Crew Lists, 1882-1959 [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2008.
Original data: Passenger Lists of Vessels Arriving at San Pedro/Wilmington/Los Angeles, California; NAI Number: 4486355
Ancestry.com. 1930 United States Federal Census [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2002.
Ancestry.com. U.S., Naturalization Record Indexes, 1791-1992 (Indexed in World Archives Project) [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.
Ancestry.com. Cook County, Illinois Marriage Index, 1930-1960 [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2008.
... and probably a few more I forgot to capture.