Could it really take 2 hours to trace a phone call?

I was born into a digital world so I know nothing of mid 1960's telephone technology. However, I find this movie quite difficult to enjoy because I am unable to believe that the phone company couldn't track a call for two hours. The coast guard was able to work faster and helicoptered the husband into to talk to his wife while out deep sea fishing. She wasn't calling from across the country or across the world, it was the outskirts of town. From the second the trace was requested at the start of the movie, they knew it was a matter of life & death. It showed everybody at the phone company doing their best to work at a frantic pace. Yes, I know in 1965 you couldn't just google a reverse directory & have the number and address in seconds, but still. Undoubtedly it might take several steps and run through different switchboards in different physical locations, yet even then it doesn't seem like more than a 20 min process. How could they bill the call if they couldn't track it???I don't think Ma Bell would become a monopoly if they didn't know how to get paid.

Sure part of enjoying a movie is the suspension of disbelief, but the entire movie being based upon what seems like a ridiculous premise is too much for me. So does anybody know anything about telephone technology of 1965? How long would it really take to trace a call?