@ixel very helpful - thank you very much indeed.
I forget how to do it via clueless though.
That remote mains switch is not for me, emits rf interference, nasty, and says you cannot use several next to one another. I might very well want to power-cycle individual modems, as opposed to the whole lot, and so that would mean having multiple units. And in any case, you say it has bad reviews.
Something that works over a LAN would be a viable option.
In any case though, the clueless method would be far better. I am not keen on power-cycling modems anyway since it takes them ages to come up, which is very annoying. Even when you just order them to reboot, using the appropriate command in the web admin ui, it takes an annoying amount of time and seems (unsurprisingly) no better than a cold boot. So presumably there is no difference due to performing vs not performing possible optional one-off hardware test sequences on cold boot only.