The Sabbeth Goy has already been mentioned, but another concept worth mentioning is the notion of what work is under Jewish law. For example, one is not to kindle a fire (hence the prohibition against lighting a fire on the Sabbath). However, one is also not to extinguish a fire either (although a candle burning down on its own and going out is OK - and Sabbath candles are lit before the moment of sunset). Why? I dunno. It’s tradition! (cue fiddle music from nearby roof).
So you can’t start a fire, but if a fire is already burning you can’t put it out (with the exception that if the fire is life-threatening PLEASE put it out regardless of whether it’s the Sabbath or not). Electricity and electrically operated things are regarded, by a process of logic that may or may not make sense to gentiles, as a sort of “fire”. Thus, you can turn on an electric light (because that’s starting a “fire”) but neither can you turn one out (because that is putting one out). BUT - if you have your electric light on a timer to turn itself off, well, under (some peoples’) rules that’s OK because you are not acting on the Sabbath to “put out the fire”. And this is where we get Sabbath elevators - you can’t summon an elevator (because that’s “starting a fire”) but if the elevator is programmed to go floor-to-floor on it’s own, well, you’re just along for the ride.
Rinse and repeat for pretty much anything electrical. Or utilizing fire. I’ve been Sabbat Goy on occasion, usually turning a stove off when the Sabbath meal is done cooking. This actually requires both understanding of at least the basics of the rules on the part of the Goy, and trust on the part of the Jew, because (in the example of the food in the oven) the Jew can not directly say “turn off the stove” because that would be initiating a string of events affecting the kindling/extinguishing of the fire.
However, preserving and sustaining life takes precedence over the Sabbath work rules, so if you have someone in your household dependent on some sort of electrical equipment in order to live (a respirator, perhaps) then turning it on/off or whatever might need to be done would be OK.
(If I have erred in any of this I’m sure one of our more studied Jewish members will correct me.)
Essentially, you’re talking about a Sabbat Goy here - except a Jewish person is not to directly initiate such a thing. So… not allowed. If, however, a gentile just happens to always be in the elevator on the Sabbath and pushes the button for your floor without being asked that would be allowed. But you can not hire a gentile to just hang out in the elevator, because, again, that would mean a Jewish person is the initiating cause of “lighting a fire”.
Honestly, I’m not sure if that would be allowed or not. Good question, and I’m interested in the answer, too, so thank you for not asking that on Friday evening so we might get an answer before Saturday evening.
That sounds like a mechanical Shabbet Goy to me, which might be allowed. It might also be defined as a golem, an artificially created servant which has a long history in Judaism. Whether or not a golem is permitted to operate on the Sabbath is, apparently, questionable - there are versions of the tale of the Golem of Prague that has the creating rabbi deactivate the golem before sundown on Friday to preserve the Sabbath, for example. But it seems to me that a golem is pretty much NOT a Jewish person so … we’re back to Sabbath Goy. Or a Sabbath Elevator.
My guess is that at least some Jewish groups would be OK with this and some would be opposed, but heck, you can say that about a lot of stuff. That’s why there are so many different Jewish groups in the world today.
Keeping Sabbath and keeping kosher are, if you will, “sister obligations” - neither is a subset of the other, they are both part of keeping the halakhah, which can be translated as “Jewish law” or “how to behave yourself”.