In his responsa on the matter, the Minchat Yizchak recounts an experiment conducted by the Chazon Ish in which he soiled his hand with ink and then ran an electric shaver over it. The Chazon Ish found that the shaver removed some of the dry ink and this convinced him it more resembled a ta’ar than a ke’ein taar. Although the Minchat Yitzchak was reluctant to condemn a widespread practice among God-fearing Jews, he was clearly unhappy about it.
Other poskim are less concerned. Rabbi Pesach Frank writes that the presence of the protective shield is sufficient basis to classify modern electric shavers as ke’ein ta’ar and to permit them.
People of exceptional piety, including mystics, do not shave their beards at all. And so I am left with the eternal mystery of my father’s chin.