“When all else fails, read the instructions” is a jocular line that has been cited in print since at least 1954, when it was applied to an automatice food dispensing machine. “If all else fails, read directions” was cited in 1956, when it referred to automatic washers and dryers.
 
“Cahn’s Axiom: ‘When all else fails, read the instructions’” was cited in a 1975 book. It’s not known who “Cahn” is.
 
 
4 May 1954, The Manchester Guardian, “Our London Correpondent: Fleet Street, Monday Night,” pg. 6, col. 4:
One stool advertised automatic dispensing machines which produce, at the drop of a sixpence, anything from hot soup to hot, cold, and mixed juices. A sign on top of one machine told the customer, “When all else fails, read the instructions.”
 
11 May 1956, Journal-Every Evening (Wilmington, DE), “Don’ts to Follow In Doing Wash,” pg. 28, col. 6:
According to the (American Home Laundry Manufacturers’—ed.) Association, there is one sure way to avoid these common washday pitfalls. When all else fails—read your instruction books!
 
14 October 1956, Milwaukee (WI) Journal, Home Sec., pt. 7, pg. 1, col. 3:
If All Else Fails, Read Directions
Learn to use washer, dryer properly, expert urge
IF YOU are planning to invest in an automatic washer and dryer, learn to use it properly.
 
Four Milwaukee home economists stressed this point over and over again as they talked about the best laundry procedures with the new automatic equipment. “As they say,” one commented with a laugh, “if all else fails, read the instructions.”
 
23 February 1957, The Daily Reporter (Dover, OH), Home and Garden sec., pg. 35, col. 1:
Don’t Forget To Read Those Directions
By ANDREW C> LANG
“When all else fails, read the directions.”
 
7 April 1957, Council Bluffs (IA) Nonpareil, “Where Many Fix-It Fans Slip,” pg. 38, col. 3:
“When all else fails, read the directions.”
 
21 April 1957, Hartford (CT) Courant, “Home Painter Urged To Read Instructions,” pg. 8C, col. 1:
“When all else fails, read the directions.”
     
Google Books
How to Read the Handwriting and Records of Early America:
The reading and interpretation of the handwriting, symbols, abbreviations, legal terminology, etc. as found in original records and on microfilm. For researchers in American genealogy
By E. Kay Kirkham
Salt Lake City, UT: Kay Pub. Co.
1961
Pg. 23:
There is a saying going the rounds now that goes like this: ‘“when all else fails, read the instructions.” It might be said in good humor here, at the end of this treatise on indexes, “When all else fails, look at the Table of Contents.”
 
Google Books
The Siege of Cancer
By June Goodfield
New York, NY: Random House
1975
Pg. 71:
Murphy’s Law: “If anything can go wrong, it will”; Cahn’s Axiom: “When all else fails, read the instructions”; Horner’s Five Thumb Postulate: “Experience varies directly with the equipment ruined.”
 
5 December 1976, The Observer (London, UK), “More About Murphy,” pg. 14, col. 3:
Cahn’s Axiom. When all else fails, read the instructions.
   
OCLC WorldCat record
When all else fails—read the instructions
Author: James W Moore
Publisher: Nashville : Dimensions for Living, ©1993.
Edition/Format:   Print book : English
 
Google Books
The Official Rules:
5,427 Laws, Principles, and Axioms to Help You Cope with Crises, Deadlines, Bad Luck, Rude Behavior, Red Tape, and Attacks by Inanimate Objects
By Paul Dickson
Mineola, NY: Dover Publications, Inc.
2013
Pg. *:
Allen’s Axiom. When all else fails, read the instructions. (U; Scientific Collections. Sometimes called Cahn’s Law.)