In Menachos 7a, we answer: The Kometz is not returned to the pit, rather, on the wall of the Kli. The Kli is shaken, and the Kometz reenters the pit by itself. It is as if a monkey put it in.
It is clear from this that a Kli Shares is not Mekadesh a Kometz put on its wall.
In Menachos 11a, Rav Papa asked:
If he stuck the Kometz on the wall of the (second) Kli, does this Mekadesh it?
(Also asked in Yuma 48a).
This was not resolved. I did not find anyone who asks this or distinguishes these.
Pesach Feldman, Yerushalayim
This is a difficult question and I will try and make a few suggestions which may enable us to answer it.
1. The Chidushei ha'Griz (7a) apparently relates to this question, and also mentions the Gemara on 11a. He seems to understand that it is obvious that the wall of the Kli does not possess the Kedushah of Kli Shares. As a result, he alludes to a different question: since the wall is not a Kli Shares, when he puts it there, why is this not equivalent to the Kometz spilling on the floor? (See Gemara below, 26b, that says that if one put the Kometz even in one's left hand, this is equivalent to spilling it on the floor and it is Pasul.)
2. The Brisker Rav answers that although the wall of the Kli does not have the status of a Kli Shares, it does possess the status of a Kli. Therefore, the Kometz placed on the wall of the Kli is not considered as though it was spilled on the floor, and it it also better than being placed in the left hand.
The way the Brisker Rav learns the Gemara on 7a may be understood with the help of the words of the Chazon Ish (Kodshim Kama 28:1) who writes that when the Gemara states that the Kli is shaken, it means that the Kohen is not holding it but rather it shook on its own. If the Kohen would have held it in his hand and tilted it on its side until the Kometz fell into the Kli, it would have been valid, similar to the case in Sukah (37b) of one who pushed the ashes of the Parah Adumah into the water, which is valid.
The Brisker Rav learns like the Chazon Ish on this point. Accordingly, the problem is not how the Kometz was placed on the wall of the Kli, but rather what happened afterwards, namely that it fell on its own into the Kli Shares.
3. In his comments on the Gemara on 11a, the Brisker Rav writes that in a similar way there is no problem that the Kometz is considered as though it fell on the floor before it reached the base of the Kli Shares. (See Rashi to Yoma 48a, DH Davkei, who implies that the Kometz essentially should be placed on the base of the Kli Shares.) However, the Brisker Rav does not explain the two sides of Rav Papa's question on 11a.
4. Here also it might be possible to elucidate the position of the Brisker Rav with the help of a different explanation of the Chazon Ish (Kodshim Kama 28:7, at the end) who explains Rav Papa's question on 11a as follows (according to the Rambam's interpretation): Somebody stuck a lot of flour on the wall of the Kli and then performed Kemitzah from the Kli. Rav Papa's question is whether or not this is considered as having done Kemitzah from a Kli.
The two possibilities which Rav Papa entertains are: (a) the wall of the Kli is also part of the Kli, and therefore the Kemitzah is valid; (b) since the flour rests in the Kli only because the Kohen is actively holding it down there, this is not considered "Hanachah" and it is not considered to be resting in the Kli.
5. We now see that the problem in the Gemara on 11a is similar to the problem in the Gemara on 7a. The wall of the Kli is considered like a Kli and is not considered like the floor. However, the question is whether there is a problem with the "Hanachah" that is required for the Kometz. The Kli afterwards is tilted by the Kohen towards the base, and according to the Chazon Ish, this is satisfactory (as mentioned in (2) above). However, there is another possible problem: Since the Kohen held the Kometz forcibly in the Kli at the time it was placed there, this is not considered "Hanachah."
Kol Tuv,
Dovid Bloom