The sentence that has a nonessential clause is " The birds, which always seem to show up at sunrise, were especially noisy today."
This refers to a set of words that go together and usually contain at least a subject, for example a noun, and a predicate with at least a verb.
This refers to a clause that is not essential for a sentence to have complete meaning, and therefore it can be removed.
Most nonessential causes are enclosed in commas or parenthesis to set them apart form the essential elements of the sentence.
Based on the above the section "which always seem to show up at sunrise" in the second sentence is a non-essential clause.
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