The minhag to dip challah into honey is only mentioned by Rosh Hashanah, however, the Mateh Ephraim (siman 601, sif 18) writes, that by the meal of erev Yom Kippur, the minhag is to dip challah into honey.
The Sefer Darkei Chaim VeSholam (siman 707) brings that the Minchas Elozor had the minhag to dip his piece of hamotzi into honey by all his meals from Rosh Hashanah until after Shemini Atzeres. It’s also brought in Orchos Rabbeinu (Vol. 2, pg. 173) that this was the minhag of the Steipler.
See also the Yalkut Gershuni (605, s.k. 3) who writes in the name of the Sefer Itim LeBinah of R’ Ginsburg (Ma’amer 15, Minhagei Chodesh Tishrei pg. 212) that he had the custom to dip his piece of hamotzi into honey by all the meals of Rosh Hashanah, and on erev Yom Kippur, Succos, and Shemini Atzeres. The Hisorarus Teshuvah (Hosafos L’Torah Moshe Al HaTorah, Mahadurah Revii pg. 129) writes that he was accustomed to dipping challah into honey on Rosh Hashanah, erev Yom Kippur and Hoshanah Rabbah.
It is known that the Brisker Rav had the minhag to dip his challah into honey from Rosh Hashanah until Hoshanah Rabbah, however, only in the middle of the meal, as he was worried about the hefsek [interruption] between the berachah and eating, since dipping is not required meikar hadin.
