Each of the functions are used by all of the types. Even Te dominants use Ti.
If you're applying it I'm inclined to think it's Te coupled with another perceiving function. Both thinking functions are concerned with studying systems. The difference is that Te organizes it's information by an external / empirical standard, Ti orders it by subjective, internally developed standards. Also, Ti does not seek to apply its information in a concrete manner. "Applying it to a novel context" implies taking literal action which is Te or Se-ish.Would studying someone else's system/behaviour and applying it to a novel context be an example of Ti or Te, either, or neither?
That's very Te and a good idea. In this example Ti would seek to understand the priests communication methods for the sake of understanding, and it would also be more concerned with establishing the validity of the priests statements and beliefs. Te sets an objective and sticks too it, ultimately information is gathered for the sake of that objective.For example, I once a knew a [possibly entj] hard-line atheist who studied how priests communicated with their audience so he could use it himself to talk about atheism.
Te again. Your logic is externally gained, internalized for decision making, then projected outward in the form of action (writing the song based on what you've studied from other song writers.) Ti would derive lyrics, structure, and etc. from purely within, very little outward reference.When I want to write a song I like to analyze the structure of other people's songs.