As the Kohen Godol only stayed in this room for 7 days, what chiyuv would there be to affix a Mezuzoh especially as nobody else used it throughout the year? Usually there is a 30 day 'exemption' period
On whom would rest the chiyuv to affix in any event?
Sholem, UK
1) This question is asked by the Gevura Ari here (by the author of Sha'agas Aryeh). He answers according to Tosfos Menachos 44a DH Talis who proves from Bava Basra 8a that for the first 30 days of renting a house it is not considered that it belongs to the renter (therefore for the first 30 days he is exempt from duites incumbent on the citizens of the city). Gevuras Ari writes that the reasoning of Tosfos applies only to regular citizens, but the Cohen Gadol is different because the Torah obliges him to leave his house and live in the Lishkas Parhedrin. Since he is obliged to do this, it makes it a fixed dwelling place immediately. If a person has a Mitzvah to do something, this means he is in the right place from the start and is never considered as a temporary resident.
2) It seems to me that the Beis Din in the Beis Hamikdash have the chiyuv to affix the Mezuzah. When the Beis Hamikdash was built in the time of Shlomo Hamelech the Mezuzah on the Lishkas Parhedrin was one of the essential parts, and it stayed up all year round, not just on the 7 days when the Cohen Gadol lived there.
Good Shabbos
Dovid Bloom