How did the eight-day celebration of Hanukkah possibly connect to Sukkot and Shemini Atzeret?

Evidence from II Maccabees suggests that the eight-day celebration of Hanukkah may have originated as a belated observance of Sukkot, a seven-day Pilgrim Festival, paired with its eighth day, Shemini Atzeret.12

In ancient times, the rituals associated with Sukkot were required to be performed in the Temple of Jerusalem during the month of Tishri. Because the Temple had been desecrated by the Seleucid king Antiochus IV Epiphanes, the Jewish people were unable to observe these festivals at the proper time.12

After Judas Maccabeus successfully reclaimed and purified the Temple, the eight-day rededication beginning on Kislev 25 provided the first opportunity for the Maccabees to finally perform the full eight-day cycle of Sukkot and Shemini Atzeret that had been missed earlier in the year.12