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> It's a lot simpler than that -- with respect to phone service, "engaged" means a busy line. "I'm sorry, your party [or 'your party's line'] is engaged," is something an old-fashioned telephone operator might say.

Telephone operators! Hey, I remember those. They always said "Number, please," in the days before dail tones were invented. Most talked through their nose, and after you gave them a number they always said "Think Q." I always sat there thinking Q until someone answered.
Howard