shyamd, many thanks. So, what I gathered from that article and media reports to date:
1) Saudis and Iranians loathe each other. Deep-seated visceral loathing. Even if they agree on many things (keep oil price high, Palestinian rights, allah ho akbar, johnnie walker > chivas regal, etc), they genuinely loathe each other and they and their predecessor "ideological guardians" have done so since AD 680 Battle of Karbala. Now you have Battle of Bahrain, Battle of Aleppo, etc etc
2) Neither Saudis or Iranians would want a war / confrontation of a magnitude that potentially endangers their respective regimes. Short of that, they will constantly jockey for superiority.
3) India's influence. As far as I can tell, its absolutely bugger all! We need Saudi oil, and millions of our citizens work in the GCC countries to earn their livelihoods; these are 'very good things' and worth preserving. We need Iranian oil, and we need access to Iranian ports and roads to be able to trade with Afghanistan; these are also 'very good things' and worth preserving. As far as I can tell the Saudis and Iranians only really need us as a customer for their oil, which we anyway need to buy.
4) Benefits to India of lower Saudi-Iranian tension. Reference to (3) above, anything that keeps oil flowing and oil price affordable (or not too unaffordable), and millions of our fellow citizens gainfully employed, is a benefit.
Having said this, I still don't see what leverage India has over Iran. Even if India refuses to buy any oil from them, they will still not give up their nuke weapons programme. For allah's sake, the Iranian regime attacked an Israeli diplomat (and Israel is our most important friend in the Middle East) in the middle of New Delhi, and what did India do? Absolutely nothing of consequence. Why? Because, we need their oil, their port, and their road to Afghanistan. Truly exposed our weakness.
And what leverage does India have over Saudi? As far as I can tell, ZILCH. The writer you referenced suggests that India exercises its influence over Iran in return for Saudi exercising its influence over Pakistan. What I don't understand is that if Saudis have so much influence over Pakistan, how the hell did the Pakistanis get away with selling uranium enrichment technology to the Iranians?
Like I said earlier, India just doesn't have any leverage to make much of a difference.
At best, India can listen to Iran and Syria, and convey to the US, Saudis and Israelis what the Iranians and Syrians are thinking, and possibly vice versa. But I don't see how India can do anything more than play 'honest broker'. There is no leverage ....