Fasting during the month of burning (Ramadaan) candles originated with the fast ordained by Adam when the days were getting shorter http://www.come-and-hear.com/zarah/zarah_8.html The story indicates Adam was not south of the Equator when he had left Eden.
Some calendar calculation rules become apparent from this, primarily that this Noachite fast does not end until the sun has passed its winter solstice which used to be on the 25th day of the stellar-month until the calendar slipped forward. This is the period when Ramadaan occurred every year during the lifetime of Muhammad SAW until the Hijri calendar was made up by Omar. From this rule it seems derived the Chinese tradition of the final month of the year always coming after the month where the Sun passes through its solstice, and the Jewish observance of Hanukkah from the 25th of the Lunar month before the solstice.
Burning 8 candles on the first day and reducing them one at a time day by day is from Shammai. Similarly the Hanukah Bush is not a new tradition but is also from Shammai from the Christmas tree, but from Adam's choice of "The World" Tree of knowledge of good and evil over the tree of life.