Its lack of relevance to the matter at hand not withstanding, I admit to be a bit bewildered by your question and thus feel the need to ask: what makes you think the pilot could possibly have any idea that trimmed parts from a bolt is what caused the stick resistance, or that he would spend the time thinking about that instead of recovering the aircraft in the few minutes he had at the most ...
Pilots have loads of checklists, many of them committed to memory. If there's a problem, there's a checklist for it and following the checklist should lead you to a solution or at least tell you what is wrong. The downside is that checklists can't account for every possible thing going wrong. A little piece of wire jamming a hydraulic system is going to be a hard fix. Even if you have the tools and access to the component, do you have time while the plane is nose down?
Planes have to be predictable, they can have massive failure states but the solution must be repeatable. Unknown failures, regardless of the severity, are a major problem and should always be tracked and investigated. A small unknown failure could be a symptom or precursor to a much larger problem.
Everyone hates paperwork but it's what saves lives.
He or she would spend time mentally running through the avionics system to think of what to trouble shoot. Experienced pilots know how their craft works just like you know how to debug a failing drive and not waste time looking at your network cable.
My neighbor is a pilot and I asked him completely off hand how to troubleshoot non responsive flaps and he went into detail about the hydraulics system, where the pumps are and the steps he would take to troubleshoot. This was off the top of his head without a checklist.
