Except when the oldest inscriptions are all from the north then it does mean something.
You are being really stubborn about this. Most historians believe the Yemeni origin of Arabs is a myth, there is very little to back it up.
"However, so far, no pre-Islamic texts in the Arabic language have yet been discovered in Yemen nor is there compelling evidence for the influence of Arabic on Sabaic, or other Ancient South Arabian languages, in Yemen proper. So while it stands to reason that Arabic vernaculars, perhaps moving south along the Ḥigāz, entered Yemen in the pre-Islamic period, evidence in support of this is lacking. It is very possible that Yemen was not Arabized in a significant way until the Islamic period"
"There is even less evidence as regards the spread of Arabic to eastern Yemen (Ḥaḍramawt), Oman and East Arabia in the pre-Islamic period. There are no preIslamic Arabic texts from these regions and, at least in the case of Oman/eastern Yemen, non-Arabic Semitic languages continue to be spoken there till this day. While no pre-Arabic languages survive in East Arabia today, the epigraphic record attests a shadowy language termed Ḥasaitic, stretching from the Ḥasā in the north to the Oman Peninsula in the south. The nomads of the Najd, Ḥigāz, and south-central Arabia produced a t large number of inscriptions in varieties of the South Semitic script which scholars term “Thamudic”. While most of these texts consist simply of signatures, the ones that do contain more often attest languages quite distinct from Arabic, and most of the longer texts remain undeciphered."