Q. Dear Rabbi.What is the source for putting some of the Havdallah wine on eyes and in pockets?
A. Remah (O.H. 296: 1) mentions that it is tradition to (slightly) wash one's eyes with the wine of Havdalah as it is considered 'Chivuv Mitzva" or an appreciation of the mitzva performed. However, on the Halachos of Kiddush (271: 10) Remah mentions that when one recites Kiddush, he should look into the cup of wine.
Mishna Berura (48) explains that it is curative for the eyes. Tur (269) quotes Rav Neturay Gaon saying hat even after Kiddush a bit of wine should be placed above the eyes. Nevertheless Kaf Hachaim (269: 6) and other Poskim maintain that during the Kiddush of Shabbos we abstain from doing so, as it may be seen as using medicine during Shabbos which in principle is not allowed.
Kitzur Shelah quotes the Arizal that when done after Havdalah one should say the verse: 'Mitzvas Hashem Boroh Meiras Einaim.' (Tehilim 19: 9 -The commandment of Hashem is clear, enlightening the eyes).
Some do so three times and also place some drops in their pockets as a good Siman and say "Siman Tov Umazal Tov Yichey Lanu Ulechol Yisrael' (Mishmeres Sholom, see Piskei Teshuvos 296: 7)
Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit'a.