Christmas cactus doesn't get plunged into total darkness like a poinsettia. Rather, in mid-September, placing it in a cooler temperature of 60 degrees with 9 hours of daylight each day is enough to signal a Christmas cactus to begin the blooming cycle. Several people claim that a northern-most room works best for them.

CSU has several articles about the re-blooming of Christmas cactus and their overall care. They all pretty much give the same information, but each article has some interesting nuances:

https://planttalk.colostate.edu/topics/houseplants/1353-re-blooming-christmas-cactus/

https://planttalk.colostate.edu/topics/houseplants/1355-holiday-cacti/

https://pueblo.extension.colostate.edu/programs/gardening-horticulture/sheries-articles/take-care-of-your-holiday-christmas-cactus/

https://arapahoe.extension.colostate.edu/2020/01/07/holiday-cacti/