What should I ask that will have the greatest possible value, given
that it's a technical position but discussing technical matters won't
be possible?
When I set up interviews for folks I'm trying to hire, after an initial phone screen, I usually have them meet with several people during their visit. I talk to these interviewers ahead of time, assign a "role" and give them an idea of what I'd like them to learn during the interview:
- Me first (since I'm the hiring manager)
- Someone to discuss and assess technical fit
- Someone to discuss and assess domain fit
- Someone to discuss and assess company culture fit
- Me last
Sometimes, I'll handle the technical/domain/culture assessment myself - depending on the nature of the role being filled and the availability of others to help.
If you aren't in a position to assess technical fit, and you aren't the manager, you might be better suited to fill the domain or company culture role.
If you are in the domain role, you ask questions related to the domain in which your company works. For example, you might be hiring a DBA to work in a Pharmaceutical company. In this role, you would talk to the candidate about the pharmaceutical industry. You would be learning what the candidate understands about the industry, if it is of interest, and if it fits the candidate.
If you are in the company culture role, you ask and answer questions as to the candidate's fit into your company's culture. For example, if you are a startup company, you might problem to see if the candidate is comfortable in a startup environment (where perhaps not everything is pre-defined, and it might be necessary to pitch in and work in areas outside your comfort zone).
Also remember that these interviewers are there to answer questions, as well as to ask them. If you have been in the company/department for a while, you may be able to provide answers to the candidates that will show them what a great company you have and why they should want to work there.
Hiring is important, particularly in a small shop. IMHO, a good hire is well worth a few hours of extra work.