rubber: To eavesdrop on conversations on the rural “party line” telephone system. Prior to the early 1990s, rural telephone lines were connected via party lines. Each telephone had its own particular ring, however there was nothing stopping an interested neighbour from picking up the phone to listen in on someone else’s conversation. The practice was so common that I recally hearing my mom talk about how, after a phone conversation ended, you would hear “a bunch of clicks as everyone else hung up.” To “rubber” was the act of listening in on someone else’s conversation.
exempli gratia: “I used to rubber all the time. That’s how you’d find out all the news.”
from the gap 
Another term for this was “rubber necking” and probably shortened to “rubbering” In my mind, I can see someone stretching their neck as far as they can to hear the other person’s conversation hence the term “rubber necking”
Thanks for that expansion and explanation, Carol!