It would be interesting to think of relations between Lebanese organization Hizbullah, and the Iranian State (and whatever political fragmentation this ‘state’ entails) as a highly complex one that does not easily fit the description of a State with a Proxy.
In this case, any Lebanese ‘local’ interest group or political organization is not a proxy but interacts in a very erratic way with its foreign partners even when they can be described as backers.
Here one needs to look closely at how the relations between the US and 14th of March members, or Saudi Arabia and Mustaqbal and other related political actors, are clearly different from the Hizbullah-Syrian relations, and the Hizbullah-Iranian relations.
Who in Iran has contacts with Hizbullah? I defy anyone to give me the correct answer. The Iranian political system in itself is a riddle; the various power struggles within the various institution is a research project in its own regard. And if we have leads, how did it change over time? The 80s and early 90s period is pretty well documented and everybody records a significant change in the nature of the relationship starting from the coming of Nasrallah as secretary general, and the gentle ousting of Sheikh Tufaili. Understanbly enough, Hizbullah in the 1980s was much more dependent on Iranian goodwill than in the mid-90s.
What scholars called the “Lebanonization process”, I would probably think of different strategies to build political momentum and organize/act successfully. Meaning that these dudes were always thinking in terms of local/territorial/political interest, but in the 1980s, it paid off to talk in “Iranian revolutionary” terms (in order to get from the Iranians much needed help, in the social sciences we call this “framing”), whereas starting from the death of Khomeini on one side, and the institutional development of the party of God on the other side, framing grievance away from the commitment to the velayet el faqih (and a lot of other things) gained more currency.
Looking at the exact political stature of each party or political actor in Lebanon can help explain its relations with other regional or international political actors. I will give a hint: In the case of Hizbullah, It is regional political forces (Syria and Iran) that are dependent on them (and not vice versa), especially since the successive political/military victory (since the liberation of the South in 2000). However, the 14th of March is weaker politically and thus needs American and other assurance that they will not loose power. Still even in the case of the 14th of March, the Americans are somewhat dependent on the fact that the 14th of March accepts to compromise with them.
For the sake of the argument, this can easily explain why Saudi Arabia would push for discussions with Iran in order to find a compromise with Hizbullah. The deadlock is local (i.e. political struggle between Hizbullah and 14th of March), and the regional forces who have interests at stake try to find possible solutions in order to keep their interest preserved. I advise to read this very good article by Nicholas Nassif that explains some of the dynamics at stake. Nassif is maybe the most interesting journalist working for Al Akhbar. He was previously a Journalist at Annahar. He also has an excellent book that draws a thorough historical account of the 2nd Bureau (Lebanese Mukhabarat).