I encourage you to drop the whole "see how they think" process. You can't read minds, and it's not possible to see how they think.
I don't like complaining without a suggestion, so... consider letting a candidate code on their own, and then ask them to walk you through what they did. You won't be disturbing the process by staring at them, and you'll get to see a bit about how they work independently & articulate what they've done. Unless you're a pairing shop, that's really what you're looking for anyway, yes?
There is no “one true way” for hiring people. It depends on the position you’re hiring for, the team, the office environment (if there is one), the project, the budget, and so many other things.
The right hiring process for one position may be completely wrong for another. And that’s OK.
I have a strong dislike for the 'see how they think' or 'code like you would in production' style instructions for take-homes - they're not specific enough.
I don't think that necessarily applies to real-time pairing exercises though. The interviewer has significant latitude to interactively question and prompt to get at the skills and values a candidate possesses.
I don't like complaining without a suggestion, so... consider letting a candidate code on their own, and then ask them to walk you through what they did. You won't be disturbing the process by staring at them, and you'll get to see a bit about how they work independently & articulate what they've done. Unless you're a pairing shop, that's really what you're looking for anyway, yes?