Get an output (like a voltage or dry contact closure) from any/most typical digital alarm clocks?
Any alarm clock that uses a buzzer or a speaker will have access to the signal there.  The connection might be wires, or it might be soldered right onto the PCB.

(So far as I know they have not integrated speakers onto an IC)

You will have to take some measurements of the signal.


Is it DC and at at least 0.8V?  Then you could boost the current with a transistor and connect it to a relay.
If it's AC you might want to add a diode to rectify, an RC low pass filter, then proceed as with the DC case.


The bigger question is this: "What home automation system does not already have a clock?"