Tracing a call is instant. It took longer back in the days when there were physical switches, but that's been a long, long time ago.
Yup. Back in the days of analog phone exchanges, you literally had to send a guy to check electrical connections between lines. Which is why it took time and which is why they encouraged the people to keep on the line as long as possible.
Digital exchanges added call tracing as a design requirement. Everything gets logged. Even if you spoofed or blocked your number, the phone company knows what you did. They are the Phone Company.
I was just reading about pirate radio stations. One pretty bitter post by a busted pirate radio operator went like "while a large number of police officers were busy chasing us through the forest, a guy got stabbed to death in the downtown. I think the raid on us was a gross mistake of police resource allocation."
This is like that, but even more petty.