It seems that since the days between Rosh Hashanah and Yom Kipur, including the eighth of Tishrei, are days of Teshuvah when many individuals have a custom to fast, the aspect of commemorating the joy of the Chanukas ha'Bayis is pushed off, and therefore Tachanun is recited.

Indeed, we find that the matter of commemorating the Chanukas ha'Bayis by not saying Tachanun is only a Minhag, and thus the Minhag can be suspended when there is reason to do so. Where do we find that not saying Tachanun in commemoration for Chanukas ha'Bayis is only a Minhag? M'Ikar ha'Din, the Halachah is to recite Tachanun and to permit fasting during the beginning of the month of Nisan, even though those are the days of the Chanukas ha'Nesi'im. The Minhag, though, is not to fast or to say Tachanun during those days, based on the practice mentioned in Maseches Sofrim (see Beis Yosef OC 429). Thus, this Minhag can be suspended when there is reason to do so, and since during the days between Rosh Hashanah and Yom Kipur it is a Mitzvah to increase our supplications to Hash-m and to involve ourselves in doing Teshuvah, we do not refrain from saying Tachanun on the eighth of Tishrei.

(By the way, the MAHARIL does not mention this reason for refraining from Tachanun during the week before Sukos. It is mentioned only by the Sefer ha'Minhagim (Rav Yitzchak Isaac Tirnauer), as cited by the REMA (OC 624:5). The author there brings an additional reason why not to say Tachanun -- because the days after Yom Kipur are days when we are happy that our sins were pardoned. It could be that this reason is the main reason, and since that reason does not apply to the days before Yom Kipur, that is why we say Tachanun on the eighth of Tishrei.)

Yosef Ben-Arza

YBA:ys