I used to observe Yom Ha’Atzmaut on BeHab, but since in recent years the Rabbanut in such years made Yom ha’Atzmaut a Nidche to Tuesday Iyyor 6th, this is now a mute point.
Please bear in mind, that BeHab is more incumbant on people who work on Chol haMoed, and hence are Mevazei Es haMo’ados. Hence no BeHab after Shovu’os, since no Chol haMoed. Since I wear my Shabbos clothes on Chol haMoed & drink a Revi’is of wine each day of Chol haMoed, I technically am absolved from having to fast on BeHab.
But question for you ItcheSrulik:- What do you do when Pesach Sheni falls on BeHab?