The "association" is all in your mind. "The lights went out AND the phones became dead". Two different clauses.
The word "AND," which you so helpfully capitalized, is precisely what creates the association between "the lights went out" and "the phones became dead." By definition. If you don't like it blame Miriam Webster, not me. And there are more than two clauses in the sentence. The important ones are "the lights all went out
and the phones became dead
because the motorcade was coming near us and no one was calling".
Later on, she makes the same association between the lights coming on and phone calls coming in: "the telephones were beginning to wink; outside calls were beginning to come in"
Absence of evidence is not evidence of absence.
An old saw that simply isn't true. Absence of evidence is most definitely evidence of absence. After, if something is absent in the first place then there will be no evidence of it being there. I think you mean that absence of evidence is not
absolute proof of absence, since there may be some unknown factor that bears on the situation under examination. Even then, this is only true if there are unknown factors.