It is good to get the aliyah of shlishi on Zos Chanukah because we read there about the immense wealth donated to the Beis HaMikdash for chanukas habayis. We say there (Bamidbar 7:84) כסף מזרקי עשרה שתים כסף קערת עשרה שתים זהב כפות עשר שנים, "There were twelve silver bowls, twelve silver basins and twelve gold spoons..." and so on. However, remember that many brachos come from being mevater, too. So, it certainly isn't worthwhile to fight over this aliyah.
This can be another answer to Beis Yosef's renowned question. True, Chanukah should be for seven days because there was enough oil for the first day, but Hashem requests that we keep an extra day, an eighth day because it is hard for Hashem when we leave.
On Zos Chanukah, Rebbe Yisrael of Ruzhin zt'l saw chassidim playing dreidel with money. The Rebbe said, "Play. What a person earns during Chanukah, he might lose. But what one gains on Zos Chanukah, he won't lose." It will remain with him forever.
The Beis Aharon (p.42) writes, "The primary miracle occurred on the eighth day. Although there was a miracle all seven days, the primary miracle was the eighth day, because it is above seven. As people say about miracles, 'Miracles are above this world.'"
The Ostrovtza zt'l said that the miracle that a lamp can remain lit for seven days had happened before. Sarah Imeinu's Shabbos lecht remained lit all week, from erev Shabbos to erev Shabbos. But a miracle for eight days happened only by the Chanukah miracle. The eighth day revealed to everyone that the miracle was above nature. It revealed that also the first seven days were a miracle beyond nature, but the primary miracle was revealed on the eighth day, on Zos Chanukah.
Every day of Chanukah, we read in the Sefer Torah the end of Parshas Naso which discusses the korbanos that the nesi'im brought when there was the chanukas hamizbeach in the dessert. On the eighth day, we finish reading all the nesi'im, and we conclude with the pesukim that discuss the menorah (which is written at the beginning of parashas Behaloscha) הנרות את בהעלתך, etc. On the final day of Chanukah, we read in the Torah what is directly related to the miracle of Chanukah. This is another indication that the primary day of the miracle was the final day.
The Beis Aharon writes, "I think the eight lamps of Chanukah are of the same concept as עצרת שמיני. Tzaddikim say Zos Chanukah is the חתימה גמר when we are inscribed for a good year."
Parashas Emor (Vayikra 23) lists the yomim tovim, concluding with Succos and Shemini Atzeres. Then, the Torah discusses the menorah (see Vayikra 24:2). The Rokeach says that the menorah, mentioned after the yomim tovim, hints at Chanukah. Chanukah is for eight days because it is alluded to next to Succos and Shemini Atzeres, which are for eight days.
Rashi (Vayikra 23:36) explains the essence of Shemini Atzeres: "It can be compared to a king who invited his children for a meal for several days. When it was time for his children to leave, the king said, 'My children, please, remain with me one more day. קשה פרידתכם עלי, it’s hard for me when you leave.'" Similarly, after seven days of Chanukah, Hashem says to the Jewish nation, "I enjoyed your mitzvos so much. Your Chanukah lecht, your Hallel, your Al HaNisim... Stay with me one more day. It’s hard for me when you leave."
About Shemini Atzeres, the Zohar (vol.3, 32.) states, "At this joyous time, the Jewish people are alone with the King. And when one is alone with the king, whatever he asks will be given to him." We can say that the same applies to Zos Chanukah. Whatever we ask Hashem for on this day will be granted.
