The Ben Yehoyada is medayak from the lashon of the Gemara לעולם יהא רגיל – “a person should be accustomed”, that one should eat the simanim by all the meals on Rosh Hashanah, since generally the word רגיל means at least three times. The Sha’arei Teshuvah (583:1) brings from the Eliyah Rabbah to eat the simanim also on the second night of Rosh Hashanah.
The minhag in the house of R’ Shlomah Zalman Auerbach (Halichos Shlomah, Orchos Halachah 70) was to eat the simanim on both nights of Rosh Hashanah, however, on the second night it wasn’t as big of a deal as the first night.
In Koveitz Ohr Yisrael (Gilyon 13, pg. 123) they bring a big arichus [lengthy discussion] of all the various different minhogim regarding the eating of simanim on Rosh Hashanah. They bring that some eat the simanim the entire Aseres Yemei Teshuvah as the inyan of ריש שתא – beginning of the year, mentioned by the Gemara refers to Aseres Yemei Teshuvah, and some have the minhag to eat simanim on erev Yom Kippur and Hoshanah Rabbah as well.