I just noticed that I do this change in pronunciation without even (and ever) noticing it, which is how I like to approach learning these rules, by pure exposure.
My experience is that "thuh" is basically a lazy / informal pronunciation of that word.
But it's also by far the most common pronunciation. "Thee" would sound strangely hyper-formal, at least in my circles.
Edit: the sibling comment (https://news.ycombinator.com/item?id=49770609) also rings true to me.
But I noticed that native speakers deviate from this at least in two cases:
1. Use thee to emphasize the following noun
2. When searching for the noun to say, they often get it wrong because they say something like "uh, thee, thee, thee, uh, book" and never sweat it.
Source: I watched a lot of Monty Python as a kid and John Cleese does this all the time.
Pretty sure it’s all vowels isn’t it?
“Thee”: apple, evening, island, offer, underpass
“Thus”: any other words where you don’t need to avoid a glottal stop to differentiate the word.