Unfortunately they won't. If you do a search on the sensors, this has
been a complaint about them since they were introduced in 2018 if I
remember right, yet have not addressed it.
Welp, after spending an hour with Google Nest Support trying to resolve
this ECO mode Home/Away problem, I've come to the conclusion that the
thermostat itself knows you have returned home (as indicated by the
app), whether via the motion detector or...
I have to back up these comments 110%.. Nest advertises the sensors as
being able to be "scheduled", but the schedule is pre-set and cannot be
changed. I cannot use the sensors to heat the upstairs bedrooms which
are colder at night without overheati...