Motzoei Yom Kippur is so much a Yom-Tov that on that evening we wish each other a “Good Yom Tov!” It is therefore a mitzvah to eat and rejoice at this time, when a bas-kol announces “go and eat with joy.”
The Rebbeim made a point of washing for a full seudah, even though they were no doubt exhausted from their strenuous avodah throughout the day. At the table they would sing niggunim and share divrei Torah.
(שו"ע אדה"ז תרכ"ג סי"ב, תרכ"ד ס"ט, התוועדויות תשמ"ו ח"א ע' 446)