Consider the following coordination of two independent clauses (joined by "but"):
Homework is due in my office hour on Tuesday, but (emphasis added) you may hand it to me earlier, e.g., in lecture on Friday.
which immediately precedes this next sentence:
I am typically in my office from mid-morning to late afternoon.
My question is: can we infer from the order of the independent clauses in the first sentence that the second sentence should necessarily be thought to refer specifically to one of these two clauses? Specifically, does "mid-morning to late afternoon" qualify the time during which the writer will be in his office on Tuesday (when the homework is due), or should that be taken as a separate remark relating to the second independent clause about handing it in early? (Ignore for a moment the clue that the first independent clause refers to the singular office "hour".)
Intuitively, I feel that a sentence which refers to a clause in a previous sentence should be assumed to be referring to the main idea of the previous sentence (in my mind the first independent clause), and that if it was intended to refer to the second clause, this second sentence should have been included within parentheses inside the first sentence, after the second clause:
Homework is due in my office hour on Tuesday, but you may hand it to me earlier, e.g., in lecture on Friday (I am typically in my office from mid-morning to late afternoon).
In other words, I feel that by placing the period between the two sentences, in interpreting the meaning, we should associate any ambiguous reference to the prior sentence with the clause of that sentence containing the main idea, which would seem to preclude choosing any subordinate clause. However, because the word "but" was used to join the sentence, I have read that both clauses are independent, and it's not clear that we can say that one is important than the other, which would seem to imply that the meaning is perfectly ambiguous.