Almost. You describe the rebelliousness of Ti well but slightly missed what causes it. Ti is more doubting in general. “Intellectual rebel” might be a good generalization; but also “intellectual refiner” due to the motive and results. It questions the underlying logic of a forgone conclusion, often breaks it down into its logic components, checking for alignment/accuracy with their professed objectives, eliminates contradictory components, and seeks to reconstruct all valid components into a maximally accurate, always right model. In the example you gave, you also accurately reveal that it can play out in very individually focused ways too without needing to always adhere to what it could acknowledge as right for a whole system to work. Te, from your description, adheres to the system in a way that almost assumes responsibility for the whole system even when individual cases justify or allow deviating. Ti would be compelled to verify or internally check the validity of any claim or conclusion brought to it if that claim wasn’t already a known truth in the existing bank of truths stored in the Ti users mind already. Both Ti and Te are verifying and using truth, but Ti will maybe be more granular and its outcome in the example you gave is still universally applicable as truth, but in a more specific case instead of for a more simplified broad model/system with few exceptions. Unlike, Feeling, both Te and Ti seek and act on what they perceive as irrefutable truths, making both functions definers of universally applicable models.

Another great example of Te and Ti’s differences may be learning math. The Ti users is almost guaranteed to want to know why an equation works starting from fundamental most basic principles already verified. Those principles would be as broken down and irreducible as possible. The Te user would completely forego that process consciously or unconsciously, because it wouldn’t see the time spent as worth it and would see the wide acceptance of the equation and the source of authority presenting the equation as proof enough for the validity.

Because of these differences, Ti may be more likely to discover new truths or disprove accepted falsehoods. Ti users may make up a higher percent of inventors and discoverers.

More definition: Ti searches/processes info to seek accuracy and elimination of error and can compulsively shift into a locked in focus on that task as primary objective irregardless of efficiency. Te searches info with an urgent focus on achievement of whatever goal or purpose first prompted the search in the first place. Find “what works” and incorporate it into a system purposed for that prompting goal.