The questions that are really about the role
Who did this job before, and where are they now. A role vacated by someone promoted is a different sell to a role vacated by someone who left in frustration, and candidates can tell the difference by the second interview whether or not you mention it.
What does this person own on their own, and what do they need permission for. Seniority written on paper and seniority in practice are frequently different, and the gap is the single most common reason a strong candidate declines late.
What does a good first quarter look like. If nobody can answer that, the role is not ready to be filled, and finding that out in the briefing call is far cheaper than finding it out after three finalists have walked.
The questions that are really about the market
Where has this kind of person come from before, in your own history. Companies usually know more about their own successful hires than they realise, and the pattern is often specific: a particular sort of employer, a particular scale of operation.
Who would you not take a call from. Competitors you would rather we left alone, firms whose people have not worked out before. This is quicker to establish at the start than to unpick after a submission.
What is the honest state of the offer. Shift pattern, travel, whether the number has room in it. A recruiter who does not ask this will find out at the offer stage, in front of your finalist.
What a rushed call costs
The cost is not that the recruiter knows less. It is that the recruiter fills the gaps with assumptions, and then screens candidates against those assumptions rather than against your actual role.
You see the result as submissions that are technically on target and somehow wrong. Everyone has the right background and nobody feels right. That is almost always a briefing problem being diagnosed as a market problem.
How to make the call worth the hour
Put the person who owns the outcome on the call, not only the person who owns the requisition. The hiring manager knows what the last person struggled with, and that is the most useful thing anybody will say.
Say the awkward parts out loud. The site that is hard to get to, the predecessor who was difficult, the team that has turned over twice. A recruiter who knows these things can position them. A recruiter who discovers them from a candidate cannot.