“I get the sense that they (Hizbollah) really prefer just to be left alone.”
When analyzing Hizbollah, it is important to appreciate that they are under the direct command of the Iranian regime.
The extreme Shi’ite sect (Twelvers) that runs Iran is focused on a final apocalyptic struggle, which they claim is almost upon us. In their view, at the end of times the “Hidden Imam” (a messiah-like figure) will re-emerge from occultation, and lead the Shia to victory - first over the Sunnis, and then the whole of the world.
In preparation, the Iranian regime deliberately set out to organize the Shia under unified command for this struggle. They established their Revolutionary Guards (Pasdaran) to protect this over-riding purpose. During the Iran-Iraq War Iran established the Quds Force within the Republican Guards, tasked with organizing supporting forces outside of Iran’s borders. Quds Forces began deploying to Lebanon in 1982 to begin initially organizing Hizbollah, which formally announced their establishment in 1985 (after conducting the Marine Corps Barracks bombing in 1983, under the direct command of Iran).
They are entirely commanded by Iran, like their Foreign Legion.
The Quds Force has since replicated the Hizbollah model within Iraq, organizing, funding, training and equipping several Shi’ite militias there (which accounted for a majority of the US combat casualties in Iraq, often with Iranian manufactured explosively formed penetrator-type munitions for IEDs). Now Iran has also established Afghan and Pakistani Shi’ite milias, which they are using as ground troops in Syria (as they did with Hizbollah, which lost more people fighting for Iran in Syria, then fighting Israel).
Hizbollah is Iran, for foreign policy or military purposes.
All good points. But remember that Hezbollah also has a political arm — and unlike other terrorist organizations, its political arm is formally recognized by many countries (even in Europe). In that regard, it isn’t much different than the dual roles played by the IRA and Sinn Fein in Northern Ireland.