I recall @Ziryab has written at least one.
Have any amateurs written books about chess improvement?

#1
Why would you want to study a book by an amateur if you can study books by world champions?
That is a good question. I think a book that shares ideas about how to study chess (and improve) whilst leading a normal life may be illuminating. GM Davorin Kuljasevic's book on studying chess, for example, is fantastic, but does focus on those spending five hours a day...
#4
Well there are books by amateurs:
Fine was a psychiatrist, Krogius was a psychologue, Steinitz, Lasker, and Euwe were mathematicians, Botvinnik and Vidmar were engineers, Tarrasch was a medical doctor, Capablanca was a diplomat, Tal was a journalist.
They all wrote books.

#4
Well there are books by amateurs:
Fine was a psychiatrist, Krogius was a psychologue, Steinitz, Lasker, and Euwe were mathematicians, Botvinnik and Vidmar were engineers, Tarrasch was a medical doctor, Capablanca was a diplomat, Tal was a journalist.
They all wrote books.
Very true! I suppose amateur is not the right word. Trying to be more precise (whilst ignoring clumsiness of expression): "Have any club to advanced strength players written about their adult chess improvement process?" (Michael de la Maza excluded).

#4
Well there are books by amateurs:
Fine was a psychiatrist, Krogius was a psychologue, Steinitz, Lasker, and Euwe were mathematicians, Botvinnik and Vidmar were engineers, Tarrasch was a medical doctor, Capablanca was a diplomat, Tal was a journalist.
They all wrote books.
All those people were also chess professionals, and the professions you list were mostly side jobs. Capablanca's diplomatic duty was touring the world to play chess and publicize Cuba. Talk wrote articles for Latvian chess journals about tournaments he played in. Botvinnik had an engineering degree but only worked during the emergency conditions of WWII and later worked on computer chess. And so on.
Tarrasch was a physician first but eventually took more and more time off for chess tournaments. Fine is the only one I know of that actually put aside his chess career to concentrate on a "real job", so most of his chess activity came before his psychology work.
#7
They were semi professional if you like.
Capablanca had some diplomatic duties in Russia, Belgium, and France.
Vidmar was nearly full time engineer involved in electrical transformers and Nimzovich complained that Vidmar spoiled tournaments for the professional players. Vidmar replied that he did not object of Nimzovich being involved with transformers.
Euwe was full time mathematician and he had full time teaching duties, but he took time off for his matches with Alekhine.
Botvinnik was also very involved in engineering in which he held a PhD. He took time off for his world championship matches.
Fine was selected for the den Haag - Moscow candidates' tournament of 1948 to designate the world champion to replace the deceased Alekhine. He chose not to participate and to concentrate on his career as a psychiatrist. He wrote his books "Modern Chess Openings" and "Basic Chess Endings" to finance his studies in psychiatry.
Lasker held a PhD in mathematics and had some important contributions to mathematics. So he did work as a mathematician. He played chess in Berlin to pay for his living while he was a student.
To come back to the original question, the book by Lazlo Polgar is maybe the answer. Lazlo Polgar was a pedagogue and he devised the training method for his daughters before their conception.
"Chess: 5334 Problems, Combinations, and Games"

One of my favorite chess books is André Bjerke (Norwegian famous writer and chess amateur): 'Spillet i mit liv' (in Norwegian).
......besides Maichael de la Maza's "Rapid Chess Improvement", which is more like a long winded pamphlet!