A while back the cable boxes in my area had a switched power outlet. I’d use a modular power supply as input to the control system. Now, most of the boxes don’t have an outlet. Those that have an outlet, don’t switch it. As a further aggravation, a firmware update might force the outlet to be always ON.

At this point most sense schemes are at risk of being broken by a firmware update or a replaced box.

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Poke around. There might be a switched USB port or TOSLINK carrier.

A very messy scheme could sense audio. Pick a reliably verbose or music channel. Switch to and monitor the audio from this channel while the system is OFF or not watching cable. If the audio stops, send a power toggle to the cable box.