Meaning of "A accompanies B"

Question

I'm struggling with the verb "accompany". Let me commence with the example first.

to go with someone or to be provided or exist at the same time as something:

[E1] Depression is almost always accompanied by insomnia.

[E2] There are two modes of establishing our reputation: to be praised by honest men, and to be abused by rogues. It is best, however, to secure the former, because it will invariably be accompanied by the latter.

The meaning says that "A accompanies B" (and "B is accompanied by A") is equivalent to "A occurs concurrently with B", i.e., there is no primary-secondary relation between A and B. But [E1] seems that it means "insomnia generally causes depression", i.e., "A causes B". On the other hand, following from the context of [E2], I guess that it means "the former certainly causes the latter", i.e., "B causes A". I'm stuck here. Which interpretation is right?

Answer 1

Your first answer is correct.

https://www.ahdictionary.com/word/search.html?q=accompany

3. To exist or occur at the same time as: dark clouds that were accompanied by rain.

In all your examples, accompany means this.

Answer 2

It's not a cause-effect relationship. Just happening, existing concurrently.