Well, since I’m not so familiar with the texts, I always hesitate to quote things. I felt that this was such a well known inyan from where I come from that I could use the quotes a bit loosely. Since you asked, I spoke to my husband and he says it comes from Pesachim 109, amud 1. I looked further in Mishna Breurah. I know that it is not halacha to have these things, but there is definitely an inyan and, like I said, I know people who wash twice a day.
Interestingly, in Mishnah Breurah, on the last page of chelek 5, it speaks about eating and drinking and mentions there meat and wine. I looked further for the explanation about the work “drink” and it says that even a person who is a ba’al teshuva and took it upon himself not to drink wine and eat meat for the other days of the year, on Shabbos, Yom Tov, Chanukah and Purim, he must eat and drink (and since the Mechaber speaks about meat and wine, then the Mishna Breurah is also speaking about them because obviously he will eat and drink other types of food on those days mentioned).
So, again, I apologize for quoting something not correctly. I will try even harder to avoid this in the future. Just as a last note, my husband did mention that the meat that the Gemara is speaking about is meat from korbonos, presumably the permissible parts of the ones that were brought when they came aliyah le’regel, like the chagigah and all the other ones that a regular person has a part that he can eat. Nowadays, since we do not have korbonos since there is no Beis HaMikdosh, then we are mesameach on wine.