> Has anyone here found ways to actively cultivate this kind relentless curiosity within themselves?
Yes; As a great fan of detective fiction specifically Poe(Dupin/Legrand) and Doyle(Holmes), I call it the "Sherlock Holmes - Dr. Watson method of interactive problem-solving" ;-)
Watson only sees the obvious, does not understand their meaning/causes/effects and starts asking questions. Holmes uses that to establish indisputable facts/evidence, reason analytically from effects to causes (i.e. the usual detective trope) or synthetically from the present to the future (i.e. prediction). Both authors in their stories often elaborate on methods of reasoning, which provide insights that can be adapted to problem-solving in general.
This is the scientific method in action viz. Observe, Measure, Hypothesize (and Model), Test, Draw Conclusions and finally, Iterate over all of the above to refine the hypothesis and minimize error.
Finally, the classic The Chemical History of a Candle by Michael Faraday is an excellent source to teach oneself/others/students/children on how to think scientifically in depth about anything - https://en.wikipedia.org/wiki/The_Chemical_History_of_a_Cand...
Modern version of the book(free) and accompanying video lectures on Youtube - https://engineerguy.com/faraday/ and https://www.youtube.com/playlist?list=PL0INsTTU1k2UCpOfRuMDR...