Etymology behind "tim-" words involving honor and "tim-" words involving fear?

Greek versus Latin, obviously. Timocracy, yes, it's in Plato's "Republic". There was an Athenian called Timoleon contemporary with him, we need more of his sort today. And then Timotheos the recipient of Paul's Epistle, as you say.

But unless I've gone completely senile, timere is the Latin verb, and the root of all the "timorous" stuff. Why your online etymology site says unknown origin I don't know. Maybe they mean they don't know its origin pre-Latin, IOW its PIE pedigree. In which case I say they shouldn't be confusing people with that stuff. Any PIE common origin, I am not competent to say, other than to note that the meanings of honour and fear are not that far apart, especially when you are talking about doing it to God.

Here's a hypothesis. The Greek and the Latin roots may share more in common than this thread suggests. Although the Latin 'timere' is usually translated as fear, it also seems possible that this meaning comes from the concept of awareness of one's innermost vulnerability. Note that 'intimacy' comes from the Latin 'intimus' a close friend - perhaps one with whom we share our most private and vulnerable self. I don't have any insight on the Greek etymology, but my guess would be that 'honor' might be close to a concept of one's true self. And if this were the case it seems like the Greek and Latin meanings might not be so far apart after all. Just a hypothesis :-)