[The series concludes, for now.]
Because it doesn't exist! There is no holiday, biblical or rabbinic, called "Simchat Torah". There is, however, a biblical holiday called Shemini Atzeret. Some observe it for 1 day and others for 2 days. The kiddush and Amidah on all day(s) of this holiday refer to it as "yom hashemini, chag ha'atzeret hazeh" (or "yom shemini atzeret hechag hazeh", depending on nusach).
Shemini Atzeret is the only yom tov that has no special mitzvot (like blowing the shofar, or fasting, or dwelling in a sukkah, or eating matzah and retelling the Exodus, or bringing an offering of new grain) beyond the mitzvot that apply to all festivals. It is MAK's favorite holiday for this reason. But many people don't feel this way about it.
Therefore, to save Shemini Atzeret (just as others, in very different times and places, sought to save Shavuot by creating tikkun leil Shavuot and confirmation), some Babylonian Jews decided to make this the time when the annual cycle of Torah reading was finished and restarted. Thus, they created the ritual of Simchat Torah. This ritual was created for the holiday of Shemini Atzeret, specifically the second day thereof (since these Babylonian Jews observed two days); it is observed on the single day of Shemini Atzeret in communities that observe one day. There is no holiday of Simchat Torah separate from Shemini Atzeret any more than there is a holiday of Zeman Cheiruteinu separate from Pesach.
With this added ritual, the second day of Shemini Atzeret has, of course, become much more popular than the first. Lots of people observe only the second day (which is d'rabbanan) and not the first day (which is d'oraita). Some communities that generally observe one day of yom tov still have their Simchat Torah celebration on the night of the 23rd of Tishrei (i.e. the night that others consider the 2nd night of Shemini Atzeret), to blend in or something.
Since I observe 1 day of yom tov, I'll be taking Tuesday off and observing it as yom tov, then hopping around to various Simchat Torah celebrations on Tuesday night (even though it will be a weekday for me, there's nothing wrong with dancing on a weeknight), and going to work on Wednesday.
I did this last year, and it meant that I didn't really get to hear the end and beginning of the Torah. I had attempted to do so a few years ago, and went on Saturday morning (the day of Shemini Atzeret) to a synagogue that I thought would be doing this (I won't name the synagogue). When I got there, I found out that they had done all their Simchat Torah stuff on Friday night, and on Saturday morning they were just doing a Shabbat service (not a yom tov service) and reading a randomly selected chunk of V'zot Haberachah, and it was a bar mitzvah. After that, I gave up on doing Simchat Torah on the day that I believe to be yom tov. So last year I went to an excellent apartment minyan on Shemini Atzeret morning. This minyan presumed the existence of two days of yom tov, but they didn't do anything that I disapproved of. They read a different Torah reading than I would have read, but "Aser t'aser" (Deuteronomy 14-16) was quite relevant to the day (except that the Deuteronomist doesn't appear to be aware of Shemini Atzeret, but we'll ignore that and read the maftir from P). (Does anyone in the blogosphere know why the Torah reading on Shemini Atzeret starts with "Aser t'aser" (rather than just "Kol habechor") even when it's not on Shabbat? I don't.)
This apartment minyan isn't happening this year. So I welcome suggestions on where to go. Does anyone have recommendations of good places to go in New York City (preferably New York County) on Monday night or Tuesday morning that will do hakafot and/or read the end and beginning of the Torah?