HERE'S PART ONE of a past-and-future survey of Yemen, "Yemen's Great Past and Future" (Yemen Times) which includes some thoughts on connections to the biblical world. I don't know much about this area, but the ancient South Arabians did not invent their own syllabic writing system. It's clearly derived from the earlier Northwest Semitic/Phoenician alphabet. I can't vouch for other details in the article, but here's an excerpt:

Yemenite expansion in Africa, in terms of population, language and scripture.
Despite the lack of unity, or perhaps due to this phenomenon, many waves of Yemenites have reportedly crossed the Bab el Mandeb straits, and settled either in the African Red Sea shore opposite the Yemenite coast, or further in the African inland.
What the famous Abyssinian legend and the great epic text Kebra Negast (the Glory of the Kings) narrate is rather an extension to the Biblical and the Quranic texts� references to the legendary Queen of Sheba � Balqis � Makeda, and to her contacts with Solomon, the King of Israel. But it reflects perfectly well the reality of the millennium-long, repeated Yemenite waves of Asiatic immigrants to the Horn of Africa area. Menelik, as son to Solomon and Balqis � Makeda, is an abstraction made for poetic reasons within the text, and it concerns all the numerous Yemenites, who repeatedly and in successive waves expressed their predilection for Africa.
It is not only literary sources and archaeological evidence that testify to this event; full epigraphic and linguistic support is offered for this assertion, since the ancient Abyssinian language and scripture (dating back to the early Christian era) have derived from the earlier attested ancient Yemenite semitic dialect and syllabogrammatic writing. Gueze, as is called the ancient Abyssinian language, is very important to Christianity, as one of the languages and the scriptures of the Evangiles and the New Testament � along with Aramaic - Syriac, Greek, Coptic, Latin, Armenian and Georgian. Gueze is the ancestral linguistic form of modern Abyssinian languages like Tigrinia, Tigre and Amharic (Amarinia) that are widely spoken in Eritrea and Abyssinia.
The name itself of Abyssinia (�-b-sh-t, Abashat) is mentioned in Ancient Yemenite texts and epigraphic documentation as the name of a � Yemenite tribe! This tribe, or at least a sizeable part of it, migrated to Africa and transferred there its name that lasts until now, as ultimate proof of the Yemenite origin of a large part of the populations of Abyssinia and Eritrea.
�Returning� the compliment, Gueze � that was never lost, since it still is the religious language and scripture of the Christians of Ethiopia and Eritrea � helped a lot in the deciphering of the ancient Yemenite epigraphic monuments. It was as useful as Coptic to Champollion deciphering Egyptian hieroglyphics. Without Coptic, Champollion would have failed; without Gueze the likes of Conti Rossini and Rhodokanakes would have failed too.

For more on ancient Near Eastern writing systems, including South Arabian ones, see this Columbia Encyclopedia article on "Afroasiatic Languages," especially the last few paragraphs.