Not sure yet if I want to chime in as an "old time grapher" ....
But in answer to your question. The then small circle of collectors would research old time players through the white pages (geez that sounds ancient) and then share the information among each other. Some addresses were available through the Hall of Fame as well as writing in care of the players former teams. I've seen some old letters too where the collector would ask for an autograph and then ask if the player knew the whereabouts of any of their old team mates.
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jim@stinsonsports.com