It was an early point of contention that became less of one over time and the contentiousness was associated with the fortunes of Ethiopia and Austria in the 1930s.

When Hitler came to power, his association with Mussolini was not strong. Mussolini had been in power for a decade at that point and was far more secure in his position. Hitler was interested in the Tirol question as well as annexing Austria to the Reich. However, Austria’s territorial integrity at the time was guaranteed by Italy. Mussolini personally assured the Austrian chancellor, Engelbert Dollfuss, of this point at a summit meeting in August 1933. In exchange for this protection, Mussolini expected that Dollfuss transition Austria to an authoritarian regime and eliminate Marxists.

Dollfuss did this in stages, being given the opportunity to do so by a Social Democrat uprising in Vienna in early 1934, which resulted in the SDs being defeated and banned. Consequently, a new authoritarian and corporativist constitution was promulgated later the same year and Austria was rewarded with a formal alliance with Italy and Hungary.

When Hitler and Mussolini met in Vienna in June 1934, the alliance between Italy and Austria was very strong and Mussolini told Hitler to leave his hands off Austria. Hitler “obeyed” but went to work on a coup in Austria to be mounted by that country’s own, technically separate Nazi Party. Hitler was betting that a successful coup would be viewed as a fait accompli by Mussolini. But the coup, which came in July, failed, despite Dollfuss being assassinated, and it failed at least in part because of a threat to intervene by Mussolini.

A turning point in the relationship between Mussolini and Hitler came with the Italian invasion of Ethiopia in 1937, which isolated Italy diplomatically. Hitler approached Mussolini for a closer alliance at that point and was embraced. This alliance allowed to no small extent for the Anschluss the following year since Mussolini withdrew his opposition. However, German absorption of Austria pushed the Tirol question to the fore.

Ultimately the solution devised allowed Italy to retain South Tirol in exchange for diplomatic support in future territorial claims by Hitler; this payoff came when Italy helped to negotiate a compromise at Munich in late 1938 over the Sudetenland. On the other hand, the agreement over Tirol also allowed German-speaking Tirolians to emigrate to Germany provider that they decided by the end of 1939. Around 85% of German speakers emigrated.

Tl;dr: Hitler ultimately traded South Tirol for Italian diplomatic support for the Anschluss and Sudetenland.

Steve Beller’s Concise History of Austria is one of my go-to texts for finding further readings on episodes like this one. More specific and very useful is Gottfried-Karl Kindermann’s Hitler’s Defeat in Austria, 1933-1934: Europe’s First Containment of Nazi Expansion. Bruce Pauley’s Hitler and the Forgotten Nazis: A History of Austrian National Socialism provides much of the political intrigue among Germany, Austria, and Italy in the 1930s. Finally, Julie Thorpe’s Pan-Germanism and the Austrofascist State, 1933-38 examines in part Austria-Italy relations and their degradation.

The specific literature on South Tirol is overwhelmingly in German, e.g., Rolf Steininger’s Südtirol – Vom Ersten Weltkrieg bis zur Gegenwart. There are shorter readings in English, e.g., Hannes Obermair’s essay “The South Tyrolean Option—A Brief Overview,” published last year in a volume of essays edited by Anja Manfredi.