Your code idea may be a case of premature optimization. Assuming 40 routers times 40 passwords; four seconds to type each one in and a four second backoff; typing each in would consume less that four hours.
You forget that he also said they don't know which accounts -- if there were multiple staff members (which I assume there were, based on the comments), you've just increased the complexity of the problem.
Personally, I'd look at using Expect (it's been a few years since I've done similar work ... there's now an Expect::Simple which might be easier to learn)
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