The Senate-House hearings into the Iran-contra scandal begin their second phase tomorrow, and we'd like to suggest some lines of inquiry the panel should pursue. Several questions remain unanswered following our own investigation, which turned up evidence of the secret arms sales to Iran as early as December 1985.

The crucial focus of the committee's second round of hearings will be President Reagan's role in the clandestine enterprise -- particularly his knowledge (or ignorance) -- of the diversion of money to the Nicaraguan contras when official U.S. aid had been forbidden by Congress. The joint committee hopes to get these key answers from Adm. John Poindexter, the former national security adviser, and Lt. Col. Oliver North, the embattled Marine who appears to have been the heart and soul of the entire operation.

But there's another line of inquiry we find equally fascinating, and more important for the country in the long run. That is the role, if any, of Vice President George Bush.

Like any vice president going for the top job, Bush has stressed his ''insider'' status in the decision-making process during the Reagan administration. Beyond that, though, Bush has made it clear that he considers foreign policy his strong suit.

Yet oddly enough, in the administration's foreign policy planning generally, and the Iran-contra ''initiative'' particularly, Bush has been The Little Man Who Wasn't There. He often sat in on the high-level meetings that dealt with the Iran deal, and as a former CIA director his opinions should have carried some weight. But as far as the record shows, Bush's principal contribution was not expertise but invisibility.

Both Secretary of State George Shultz and Defense Secretary Caspar Weinberger voiced their opposition to the misguided venture -- and there's documentary evidence to prove it. Even John McMahon, then deputy director of the CIA, opposed the plan. And one of the most active participants, former national security adviser Robert McFarlane, came to oppose it.

There's not a word in the record, however, indicating that Bush uttered any warning or misgiving about the initiative. Nor is there evidence that he did much in support of it, beyond submitting a memorandum detailing a meeting he had in Jerusalem last July with an Israeli official. At no point is there the faintest suggestion that Bush gave the White House the benefit of his extensive experience in foreign policy, clandestine operations or domestic politics.

The activities of Bush's national security adviser, Donald Gregg, have come under committee scrutiny, and he is expected to testify. Bush had to revise his account of Gregg's meetings with a onetime CIA operative -- who also met three times with Bush -- and the topics they discussed.

Before the vice president is placed on the griddle, directly or indirectly, the future of the lame-duck president will be dealt with, and Ollie North is the witness who will have the greatest impact on President Reagan. Aside from the obvious questions raised by the first round of hearing witnesses, here are some that should draw interesting responses from North:

Did North, as he bragged in early 1986, secretly mastermind a Customs Service ''sting'' that nabbed 17 people in an alleged conspiracy to sell arms to Iran? If so, did he do it to eliminate competition for his own arms-for-hostages deal?

What does North know about the pivotal role played by the late CIA director, William Casey? Was it Casey who suggested diverting profits from Iranian arms sales to the CIA-backed contras?

Why didn't North, whose boss Poindexter was a Navy admiral, ever tell the Navy of his secret arms sales to Iran? As we reported, the Navy, in an honest effort to save money, was dickering to buy back some aircraft testing equipment sold to Iran under the shah. But the Navy broke off the negotiations when Iran asked for missiles in return. Was North afraid a straightforward Navy/Iran deal would queer his own sale of missiles to Tehran?