When should "only" come before a verb phrase?

I’m really struggling to understand when and how to use “only” as an adverb — and how its use is impacted by verb phrases. The following post on English StackExchange doesn’t really clarify it for me: Correct position of "only". I understand that placing “only” in different places modifies the meaning of the sentence, but when should you use the word to modify a verb phrase?

In a Quick and Dirty Tips post, the writer states that the stress can be a deciding factor but that “…it’s still better to put ‘only’ as close to the word or phrase that it modifies…” My confusion arises from the phrase part. For instance:

1. Gary realized that he was wrong only after he had left.
2. Gary only realized that he was wrong after he had left. (“Only” before verb phrase)

In other words, Gary thought he was right about something, but realized at a later stage that he was actually wrong.

Which of the two sentences conveys the correct meaning? Can both be correct? English isn’t my first language, and this type of construction is really difficult for me to understand.