Earlier quoted context omitted.
Generally to get candidates who are like this to open up, I simply assert: "Tell me what you are thinking about right now" "What is jumping out at you for you to be stalling?" "Did you see something?" --> "Why?" --> "You seem to be quiet and deep in thought, what are you thinking about?" etc...
That sounds awful, you are actively sabotaging someone by ruining their concentration while they're trying to solve a bug in unfamiliar code under time pressure. This is like having a manager requesting status updates every 10 minutes when you're trying to fix a production failure. Even if I solve the problem I'm walking out of that interview with a very negative opinion of your company.
You're not bothering people while they're taking an expected amount of time to look at it. You're stopping a several minute silence after handing someone a basic loop and if statement.
For most positions we're talking about, this should not be a major problem. I found when doing something similar people either looked at me like I was crazy for giving them such a basic problem and after being reassured there was no catch answered simply and clearly, or just couldn't do anything. Followup questions about the code then went terribly (e.g. a JS contractor asking for £500+/day who didn't know what the difference between global and local variables was, why you should put var in front of things, etc).
These things are often good to weed out the incredible number of people who seem to have little to no coding ability at all for jobs where that's an obvious pre-requisite. I've also had people fail to solve a basic problem (roman numeral generator or reader) at home in whatever language they wanted, not even getting vaguely close. One person even sent in their broken version pasted into a word document.