Gemara

Mishnah: Worn out Michnesayim and Avnetim of Kohanim were used to make wicks for the Simchas Beis ha'Sho'evah.

52b - Beraisa: A woman was able to select wheat by the light of the Simchas Beis ha'Sho'evah.

Shabbos 21a - Beraisa: The wicks forbidden to use on Shabbos may not be used in the Mikdash, for it says "Leha'alos Ner Tamid".

(Implied question: How do we learn this from the verse?)

Answer - Rami bar Chama: The verse teaches that the flame must go up by itself without anything to help it.

Question (Mishnah): Worn out Michnesayim and Avnetim of Kohanim were used to make wicks for the Simchas Beis ha'Sho'evah. (The Avnet is mostly of wool. Woolen wicks may not be used for Shabbos, for they do not draw the oil well, and one might come to tilt the lamp!)

Answer: The Simchas Beis ha'Sho'evah is different. (Leha'alos Ner Tamid applies only to the Menorah.)

Question (Beraisa): Worn out Bigdei Kehunah were used to make wicks for the Mikdash.

Suggestion: Even Bigdei Kehunah with wool were used!

Answer: No, only linen Begadim were used.

Yoma 23b - Beraisa - R. Yehudah: "Yilbash Al Besaro" is extra to obligate the Kohen to wear the Mitznefes and Avnet during Terumas ha'Deshen;

R. Dosa says, it permits Bigdei Kohen Gadol of Yom Kipur to be used afterwards by a Kohen Hedyot.

Objections (Rebbi): The Avnet of Yom Kipur is unlike the Avnet of a Hedyot! Also, Begadim used for a great Kedushah may not be used for a lighter Kedushah!

Rebbi: Rather, "Yilbash" allows using deteriorated Begadim. "V'Hinicham Sham" requires Genizah for the Bigdei Lavan of Yom Kipur (they may not be used again).

R. Dosa says, "V'Hinicham" forbids a Kohen Gadol to use them on another Yom Kipur, but a Hedyot may use them.

Kidushin 54a - Beraisa - R. Meir: Me'ilah applies to worn out Bigdei Kehunah.

Avos d'R. Noson (41:12): The following were put in Genizah -...Bigdei Kehunah, Bigdei Kohen Moshi'ach...

Rishonim

Rambam (Hilchos Klei ha'Mikdash 8:5-6): Deteriorated Bigdei Kohen Gadol are put in Genizah. Bigdei Lavan worn on Yom Kipur may not be used again. They are buried where he took them off, and one may not benefit from them. Deteriorated Michnesayim and Avnetim of Hedyotos are used for wicks for Simchas Beis ha'Sho'evah. Worn out Ketonos of Hedyotos are used for wicks for the Menorah.

Source (Griz Kerisus 5b DH b'Rambam (p.75)): Avos d'R. Noson says that Bigdei Kehunah and Bigdei Kohen Moshi'ach were put in Genizah. 'Bigdei Kehunah' must be of a Kohen Gadol (Merubah Begadim), for worn out Bigdei Hedyot are used for wicks. This is not a special law of Bigdei Kohen Gadol. Rather, all Klei Mikdash that wore out require Genizah.

Kesef Mishneh (6): The Rambam holds that the Avnet contains wool, therefore he allow wicks from Avnetim only for Simchas Beis ha'Sho'evah, which is not mid'Oraisa, but not for the Menorah. He allows wicks from Ketonos, and the same applies to Migba'os. Alternatively, the Migba'os were thin and not suitable for wicks.

Question (Tosfos Sukah 51a mi'Bal'ei): The Mishnah teaches that worn out Michnesayim and Avnetim were used for Simchas Beis ha'Sho'evah. Why does it omit Ketonos?

Question (Tosfos Yom Tov Sukah 5:3 mi'Bal'ei): Why does Tosfos ask about Ketonos, but not about Migba'os?

Note: Perhaps Tosfos holds that the Migba'os were thin and unsuitable for wicks, like the Kesef Mishneh.

Answer (Tosfos Chodoshim Sukah 5:3): The Tana refers to Begadim of Stam Kohanim. He teaches that the Avnetim of Hedyotos were of pure linen (and are good for wicks), and that Michnesayim are not a disgrace to the Mitzvah, even though they are to cover Ervah.

Rambam Hilchos Me'ilah (5:14): Me'ilah applies to worn out Bigdei Kehunah.

Question (Mishneh l'Melech): Me'ilah does not apply after the Mitzvah was done!

Suggestion: Perhaps we learn all Bigdei Kehunah from Bigdei Lavan, for which (we learn from "V'Hinicham Sham" that) Genizah is required after the Mitzvah was done!

Rejection: If so, even Bigdei Hedyot would require Genizah. We learned that they are used for Simchas Beis ha'Sho'evah!

Suggestion: Perhaps they indeed require Genizah, but nevertheless they may be used for Simchas Beis ha'Sho'evah because it is a need of the Korban!

Rejection: If so, the same should apply to used Bigdei Kohen Gadol!

Summation (Mishneh l'Melech): Indeed, the Yerushalmi says that worn out Bigdei Kohen Gadol were used inside (for the Menorah), and worn out Bigdei Hedyot were used outside (for Beis ha'Sho'evah). Surely, mid'Oraisa there is no difference; Chachamim designated the more Kodesh clothes for the Menorah. However, the Rambam holds that the Bavli disagrees. The Bavli learns about Bigdei Zahav from the Bigdei Lavan, and forbids all use of Bigdei Kohen Gadol. Since we do not learn Bigdei Hedyot from Bigdei Kohen Gadol, what is the source to forbid Bigdei Hedyot after the Mitzvah?

Question (Yerushalmi): The oil and wicks were of Hekdesh. Why were people allowed to benefit from light of the Simchas Beis ha'Sho'evah? There should be Me'ilah!

Answer #1 (Yerushalmi): Me'ilah does not apply to sounds, sights and smells.

Objection (Tosfos 53a DH Ishah): (The Bavli holds that) even though there is no Me'ilah, it is forbidden to benefit from them!

Suggestion: Perhaps Beis Din stipulates that this will be permitted (from the beginning the Bigdei Kehunah and oil were not totally Kodesh)!

Rejection (Tosfos Shabbos 21a DH Simchas): There is no reason for Beis Din to stipulate thusly.

Answer #2 (Tosfos Shabbos ibid.): Since it is to honor Nisuch ha'Mayim, this is considered a need of the Korban - "U'Sh'avtem Mayim b'Sason".

Question: Flutes at the time of Nisuch ha'Mayim are needed just as much for the Korban, nevertheless they do not override the Isur mid'Rabanan of instruments on Shabbos. Why were Chachamim more lenient to permit using Hekdesh, an Isur Torah?

Answer (Mishneh l'Melech Hilchos Klei ha'Mikdash 8:6): Indeed, Tosfos answers that honoring Nisuch ha'Mayim is considered a need of the Korban to justify a stipulation of Beis Din.

Answer #3 (Tosfos Sukah, ibid.): The Gemara means that there was enough light to enable a woman to select wheat (but it was forbidden to do so).