Sure; it's just like the J2 marker: upon being positive for it, one must check if it is of Jewish origin. But many non-Jewish Cretans, Lebanese, Syrians, Iraqis, Iranians, Armenians are also positive for J2. So is my T of Jewish origin? Could be, based on the fact that it is the T marker. But T probably originated 30,000 years ago on the Iranian peninsula. J2 originated between southern turkey and northern Iraq. As for how my particular subclade clusters, I suspect a Phoenician origin as the only other people I know with T-PF7443+ are from Mediterranean Europe (a southern spaniard, a canary islander, a southern Sardinian, me).
These locations were all visited by the Phoenicians of Lebanon. In fact, everywhere where the Phoenicians visited has slightly inflated T frequencies. Also, I am a T1a variant, which could be signal of Neolithic arrival too Europe some 5,000-10,000 years ago; most T1b's though (downstream) are associated with medieval Jews in Europe. I for one, have no known Jewish ancestry and I've tested on ftdna for this. Take P-77 for example; it is very present in mizrahim Jews (Iraqi, Kurdish and Iranian Jews) that never left the Middle East. This could mean the T marker was brought there via the general Canaan/levant region. Within T-P77, according to ftdna, you'll get different clusters made up of Ashkenazi Jews, mizrahim Jews and other non-Jewish populations (Jordanians, Saudis, Kuwaitis and Omanis).