The "CL" stood for "Clinton"????
Neighbors would get impatient and start clicking the phone to encourage us to get off the line.
I remember our two digit number staying the same when we switched to a live switch board. My friends mother became the switchboard operator so I got to go in and watch. There were phone jacks, all numbered to plug into. She then became the only person who could listen and get the latest news, i.e. births, accidents, ectera.
If you grew up in New York State CL likely stood for Clinton. DeWitt Clinton was an early governor of the state and I think it is also the name of a county.