Having a bit of a hard time finding a straightforward answer to this question, only convoluted roundabouts. Any information would be much appreciated!
Edit: have found some acts including bombings of Italy’s own civilians in order to blame the left wing. Also seen a little bit about “a strategy of tension”.
Another question: if the red brigades were considered to be left wind, then who were the right wing of Italy’s government during this time?
The issue with Gladio is that its history can be linked to three broadly overlapping concepts involving a multitude of variously interlinked actors, with many crucial details still classified, poorly documented, or corrupted by a partisan agendas.
The three broad themes are: The American plans for the original "Gladio;" if and how the Italian authorities modified and weaponized of that plan; and any autonomous action by local extremist organizations.
It is undeniable that there was a project to establish covert NATO-coordinated stay-behind forces in Western Europe which was codenamed "Gladio." The idea was that small cadres of specially trained troops would access hidden or undocumented weapons caches and organize resistance movements behind enemy lines in the event of a Soviet invasion of Western Europe. While some weapons caches were indeed established, the program seems to have petered out fairly quickly and never mutated into the sort of false-flag operations needed to implemented a deliberate "Strategy of Tension." Indeed, the conflation between Operation Gladio and terrorist activity in Italy is actually almost wholly attributable to a single work by the Swiss historian Daniele Ganser at the University of St. Gallen, who published "NATO's Secret Armies: Operation Gladio and Terrorism in Western Europe." The fundamental problem with that book is that it is based on the US Army Field Manual 30-31B, which in all probability is a piece of Soviet disinformation propaganda produced in the early 1970s, just when the "Years of Lead" were starting (Field Manual 30-31 is an intelligence manual, which can be construed to be related to the concept of False Flag operations, but not exactly to the point where its appendix B would be dedicated entirely to them; and also, why would an entire operation be run out of a Field Manual appendix?).
Where Operation Gladio did contribute to the "Strategy of Tension" was that the Italian security apparatus (and politicians close to the security apparatus) now knew that there were hidden weapons caches all over the country. Since these weapons catches were not exactly crates buried in the woods, but were more typically simply undocumented or uncatalogued weapons stores located in existing military depots, significant questions emerged when those weapons found their way into the hands of terrorists.
How these weapons found their way into the hands of terrorist organizations is a topic of major contention which still surrounds the "Years of Lead" in Italy. Was it a deliberate operation by the Italian security apparatus? Was it the doing of disgruntled or radicalized individuals within security forces? Or, due to the covert nature of these weapons stores, did the Italian Army simply lose track of them?
There is no doubt that the last two thirds of the 1970s were not a happy time for Italy. The middle eastern Oil Crisis of 1973 had revealed deep flaws under the surface of the country's industrial system as economic growth slowed down significantly, while a new policy of detente between the United States and Communist powers risked to delegitimize the conservative Italian ruling class (for many, but not all, of whom anti-communism had become a convenient shorthand explaining why they needed to remain in power at all costs, and also because "The United States asks this of us" had become the standard explanation to anyone who might have follow-up questions).
As for your question on what was the Left and what was the Right in Italy at this time: I'm always hesitant to insist on a differentiation between what is "Left" and what is "Right" in politics. Generally, the "Left" will want change, while the "Right" wants to conserve the status quo. But from one political system to another, what constitutes "Change" and "Status Quo" will dramatically differ, so what is considered a "Right Wing" or "Left Wing" stance in one system might not translate well to another. As an example, in some economies public expenditure or nationalization of industries is considered a "Left Wing" policy. However, in Italy the long-governing Christian Democracy party oversaw postwar nationalization programs which some some estimates postulate placed over half the economy under state control. This was coupled with generous social welfare programs. The largest parliamentary opposition to the Christian Democrats came in the form of the Italian Communist Party, which instead often argued against expanded public expenditure ("austerità di sinistra") and could even prefer welfare be delegated to local associations and unions instead of in the hands of the state. Who is "the Left" and "the Right" here? And given that the Italian electoral system always used proportional representation, what to make of the countless smaller parties with which the larger parties needed to collaborate in order to create majorities at both the national and local level?
My point is that organizing political parties along a left-to-right spectrum can be a useful shorthand, but more often than not policy positions and decisions will be the fruits of a combination of the preferences expressed by that party's voters, the platform and ideas brought forward by the party's members, as well as the limits of what is possible in a given political system, rather than the fruit of a fixed Left-Right alignment. The aforementioned Communist Party aversion to public sector spending, for example, disappeared in those city and town councils where the communists were able to garner a majority. This was not perceived as a particularly inconsistent practice: the Communist Party positioned itself as a champion of the working class and in favor of collectivization and direct democracy; where the Communist Party held a majority, so it followed that public sector initiatives were true expressions of the public will; where the Communist Party did not hold a majority (such as the national stage) public sector initiatives were an expression of bourgeois democracy. There were of course shades of nuance, as the communists could coalesce with other like-minded parties (such as the Socialists, Social Democrats, and even at times the Christian Democracy party) to endorse initiatives at both the local and national level, but at all times the Communist Party angle was that their actions were an expression of the will of working-class Italians. So while this is a convoluted way to grudgingly concede that we can call the Communist Party the "Left," direct democracy and worker enfranchisement was really the driving idea behind the Italian Communist Party's political stances, while the Christian Democracy party (the "Right") presented a platform based around "Christian Charity" but also defended the values and interests of the socially conservative middle and upper class. But we can even complicate things further, as the large Christian Democracy party housed various internal "Currents," which could themselves be defined as "Left Wing" (pushing for parliamentary coalitions with the Social Democrats, Socialists, and why not, even the Communists) or "Right Wing" (pushing for coalitions with the Liberal Party, the Republican Party, and why not, even the neo-fascist Italian Social Movement).
How this dynamic changes in the late 1960s and led to the emergence of terrorist activity during the "Years of Lead" follows after the jump.