dial tone detect circuit
If your device simply detects the line voltage, you might be able to easily fake this with a jumper somewhere inside the device, with a little reverse engineering.
There would be some circuit monitoring the voltage between the tip and ring, likely a very simple circuit,easy to trace and reverse engineer. Optocouplers are common for this purpose, but its not a certainty. Sometimes the voltage is rectified, in case tip and ring are reversed.
If the device is powered by the telephone line, there will be a power supply circuit to figure out (unless the device is very simple, that is, has no integrated circuits) but with luck it will be a simple 3 terminal regulator.