We have a few local telephone directories from the past. They have been been indexed, and you can search for names or numbers within them by using the search tool in the viewing window. Click on the year you want to view, then you can click on the box at the lower left of the displayed phone book to make it full-screen for easier reading. The search option may be used as well.
Arizona directories can be found on the Library of Congress website at https://www.loc.gov/collections/united-states-telephone-directory-collection/?fa=location:arizona. They have digital copies of Jerome phone books, which include Clarkdale, from 1930 to 1957.