I've scoured a boatload of sources but it's like the kid was a ghost. That may be because he died so soon after dad became emperor and until then he was JUST ANOTHER archduke. But I've also asked around, and even Urbanus VII (who's usually pretty good at chasing down leads - and I figured for his original Isabelline Age TL he might've come across something) couldn't really be of much help.
As to your idea of what Johann Karl was like, he could well have been as you describe, but my money's on him being dad 2.0. The reason I say this is because Ferdinand III (like Leopold I) wouldn't have been surrounded by yes-men his whole life. Johann Karl/Ferdinand IV is the eldest son and heir, somebody that the courtiers are going to agree with even if it kills them, their younger brothers would've both spent their formative years with the spectre of a clerical career hanging over them, but also being curbed and stood-up to by tutors, rather than being given entirely their own way. That means that their personalities were already formed by the time they became heir. JK is heir from the moment of his birth (if not to the Empire, at least to his dad's portion of Austria), different kettle of fish.