Answer:
I) adverbial clause
ii) it tells us when the action took place
The grammatical name is given to this expression is adverbial clause and Its function is to tell us when the action took place.
Adverbial clause is an adverb which is a dependent clause. It's used as an adverb in a sentence to show the time, contrast, conditions, place, reason, concession, purpose or result.
The adverbial clause of condition usually starts with the words if or unless. This states the condition for the main idea to come into effect.
Moreover, according to the sentence 'while we sat holding our breath' is a adverbial clause because it represents a condition and place or the reason.
At the end, it provide us about particular action about the person who sat holding his/her breath.
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