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A butt phone is a device used by technicians (and rarely ever home users) working on telecommunications networks to diagnose issues within the communications systems.

All the numbered buttons and the plugs etc are located on the end of the handset itself. Hence, the term butt phone.
Example 1:
Technician: "I have my butt plugged into the line"

Example 2:

Technician: "I love my butt phone"
by HotWater February 27, 2012