The Gemoro says (48a) that for someone living in Chutz La'aretz who must eat in a small Sukka on Simchas Torah (due to lack of alternative place to eat) should bring in the Ner. Since during Sukkos he does not bring in the Ner, this will be a Heker that he is not adding to the Mitzvah of Sukkah.
My question is that the reason for not bringing in the Ner during Sukkos is because of danger of fire. How can we recommend that he bring in a Ner for Simchas Torah?
Meir Eliezer Bergman
Tosfos on 29a gives your reason for not putting a light into a small Sukah. Rashi (there, according to Darkei Moshe (OC 639:2) and Bach) however, seems to learn that the reason is because a Ner of Cheres is usually dirty.
The Magen Avraham (639:2) says that the reason we are Choshesh for the Sukah catching fire is because this may lead to a person being in a position where he is unable to keep the Mitzvah. Perhaps there is not a real worry that it will catch fire, but rather an extra precaution to ensure the upkeep of the Mitzvah. This reason is not applicable on Shemini Atzeres, even though we are discussing Chutz la'Aretz where one must eat in the Sukah on Shemini Atzeres; since it is only due to a Safek or a Minhag, we are not Choshesh.
The Ravya (641) understood that the problem with a Ner is not that it will actually catch fire but that he will be nervous of it catching fire and will therefore leave the Sukah, but our Tosfos does not seem to mean this Pshat.
For other Pshatim, see Ba'al ha'Ma'or and Ri mi'Lunil.