If you want to try to make it bloom, you can place it outdoors for a few weeks, as long as the night temperatures don't drop below 55Ã‚Âº F. The cool night temperatures stimulate bud set. It's a little late to do this ... September 1st has always been the date I put my holiday cacti outside ... but you might have a flower or two for New Year's or shortly after.
I would leave the long branch on it for now. In the spring, you could take it off and use the leaves to start more plants. I would probably separate it at the joint just below where all the new leaves have sprouted, and use that entire end to start a plant. More branches should sprout from the end of the leaf on the old plant.
If you prefer, you can give the plant 16 hours of darkness, instead of the cool night temperatures. I find that more difficult, because almost invariably, I suddenly desperately require something that is stored in the closet or cabinet where I've stashed the plant. Opening the door, of course, disrupts everything. I also don't keep particularly regular hours, so I always worry that I'll get busy with other things and completely forget about the plant, only to discover it by accident months later.
You can just cover the plant with a box or tub, instead of placing it in a closet or cabinet, but I know myself well enough to know I'd still probably forget about it,
Either method works quite well, though, to encourage holiday cacti to bloom. Last year, my holiday cacti all began to bloom just before Thanksgiving, and didn't stop until April of this year.
This year, however, I'm experimenting with a different method. I have all the holiday cacti in my south bedroom, which is unused at the moment. The room is unheated and the windows are open, so they're getting the cool night temperatures, as well as the natural daylight for this time of year. That isn't 16 hours of darkness, but the plants don't require both conditions in order to set buds, either one alone will do the trick.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams