I agree with tommyr2006 in his 2007 post. The trigger is cooling temperatures, not light. These are tropical plants so they get about the same 12 hours of light and dark year 'round. However, temperatures and rainfall change in the tropics.
My X-mas cactus is more than 50 years old - I got it from my grandmother in the '60s. At one point it was several feet around and no longer "house broken". So, it got a drastic makeover, giving me dozens of plants to give away.
My holiday cactus (T-day, X-mas, and E-day) spend the summer outside in very bright shade. I water and fertilize regularly during the summer. As night time temperatures cool in September, the plants begin budding. I bring them into the house 2 weeks before turning on the heat, placed in a bright, west facing window. They begin to bloom in Nov and go through Dec.
After bloom, I reduce watering and allow them to rest until early spring with only monthly watering. My plants are in homemade compost with plenty of grit.
I also have one VERY old Christmas Cactus. It's from a cutting I took in 1970 from an older relative's massive plant. I have no idea how old that plant was, but it certainly had been there many years.
I also have two newer Thanksgiving cactus which grow very well indeed and are covered regularly with massive flowers.
I put all of them out in my screened porch for the summer, but unlike you, I tend to ignore them, watering only when I remember. When I bring them in around the time of our first frost, they are generally covered in buds or beginning to set bud. For my old one it's advantageous if it hasn't set buds because they are likely to twist themselves off if I don't get the light just right - nearly impossible since the porch is on the north side of my house and my LR faces south.
They now reside on plant stands in the south window and generally bloom again in the spring. I used to put them on shelves next to my east window until they became too large to fit.