Pulling a clock radio apart, jim11662418 found a separate printed circuit board containing a radio receiver that picked up signals from Fort Collins, Colorado, transmitting a time signal.
This was connected to the main board with three wires, so [jim11662418] decided to replace it with an ESP8266 board that connects to the internet via WiFi, using NTP (network time protocol) to get the time.
This simply involved connecting theESP8266 to the two digital lines, and writing some code that mimics the responses from the original radio receiver.
However, a WWVB signal simulator would avoid the need to modify each clock.