I believe a frame challenge is necessary, as the underlying assumption of the question, and in particular the material quoted from another answer, is, I understand, incorrect.
This assertion, in short, is that if an invocation of the 5th is challenged, or perhaps just "hard to understand (the validity of)", then the judge may privately question the one asserting the right for more specific details. And from there they may then make the determination of the whether the invocation is valid. I've heard this logic many times myself, and have had it enter my head as fact at some point or another. It seems one of those persistent folk tales about the legal world.
My best guess is this stems from how the limits of the 5th amendment protection on self incrimination are typically phrased within major decisions, or popular summations thereof (including but not necessarily limited to, or specifically implicating, wikipedia pages). The phrasing I am most familiar with is "an invocation of the 5th is valid if the person has a reasonable fear that the answer may be used against them in a prosecution"; perhaps modified, more accurately reflecting the jurisprudence, to add "or as a link which could lead them to evidence that could be used in a prosecution against them".
The mistake then arises in applying an everyday understanding of this phrasing: how else are you to decide if a person is being reasonable unless you question them? Maybe they've got a good reason, maybe they have a psychotic delusion, maybe they're just trying to mess with the court for their own amusement, etc. etc. Surely you have to investigate to find out.
But within American courts, the term "reasonable" in such a standard almost never invokes the everyday understanding like this. Instead, it refers to some abstract and generic entity. A "reasonable jury" is not a judgment made about the particulars of a given jury, but rather an artificial construct created within the mind(s) of the judge(s) composed of purely hypothetical and generically "reasonable" everyday people. And the legal standard to uphold that the "reasonable" standard has been met is not whether the particular person/jury/whatever at hand was acting reasonably in the usually understood fashion. But rather if such an imagined being/group/whatever could possibly act in such fashions.
As such, if a Judge is considering overruling an invocation of the 5th, they must invoke such an abstracted entity, within the context at hand, and see if they can construe one who reasonably invokes the protection. The judge may be able to use certain facts about the particular entity at hand, depending. If you are invoking the 5th and the record already shows you have an extensive criminal record, the court may consider that this reasonable abstraction also has an extensive criminal record; at which point it may become clear that such a person may wish to invoke the 5th so as not to incriminate themselves in other crimes. Even moreso if the context is a far-ranging federal grand jury investigation into organized crime, and the questions you invoked the 5th on regard your connections to events of established interest to this investigation. And this is done without actually further questioning the person, beyond what is already in the record. All the court has to do is imagine some reasonable person with a reasonable fear within the context at hand; if it can, the invocation of the 5th is generally to be sustained. No actual determination of the particular person's "reasonableness" is required, or really even permitted.
All of the latter hypothetical was essentially the fact of the matter in the case Hoffman v. United States. It is a very interesting and informative read, and I think fairly accessibly written (as long as one isn't too easily thrown off the rails by the citation formatting). It covers a great deal of how any potential challenges to the 5th are to be handled. And the short is as I have indicated above: an abstract "reasonable" person is constructed, with such construction informed by the circumstances and knowledge at hand, and judgement of reasonableness made from there. It specifically points out that courts should be mindful of the fact that some people earn a living by violating and evading the law, and they are protected by the 5th as thoroughly and strongly as anyone else is, so the courts should consider the question of whether it would be reasonable for such a person to have invoked the 5th when deciding if it should be upheld.