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Taken form encyclopedia britannica online

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The Minaean kingdom (Maʿīn) lasted from the 4th to the 2nd century bc and was predominantly a trading
organization that, for the period, monopolized the trade routes. References to Maʿīn occur earlier in Sabaean texts, where they seem to be loosely associated with the ʿĀmir people to the north of the Minaean capital of Qarnaw (now Maʿīn), which is at the eastern end of the Wadi al-Jawf and on the western border of the Ṣayhad sands. The Minaeans had a second town surrounded by impressive and still extant walls at Yathill, a short distance south of Qarnaw; and they had trading establishments at Dedān and in the Qatabānian and Hadramite capitals. The overwhelming majority of Minaean inscriptions come from Qarnaw, Yathill, and Dedān, and there is virtually no evidence of territorial possessions apart from the immediate vicinities of these three centres, which have more the aspect of typical “caravan cities.” A thin scattering of Minaean inscriptions has been found in places just outside Arabia, such as Egypt and the island of Delos, all manifestly resulting from far-flung trading activities; and texts from Qarnaw refer to a number of important points on the caravan routes, such as Yathrib (Medina) and Gaza, and also to interruption of trade by one of the several phases of warfare between Egypt and the Seleucids of Syria. An explicit mention of caravans is perhaps found in the expression mʿn mṣrn, interpreted by the scholar Mahmud Ali Ghul as “the Minaean caravaneers.”

Minaean social structure differed from that of the other three, predominantly agricultural peoples. The latter were federations of communities (often termed by modern scholars “tribes,” though they were not genealogically based) grouped under a leading community, with the nation as a whole designated by the name of the hegemonial community, followed by the phrase “and the [associated] communities.” The Minaeans, however, were subdivided into groups of varying size and importance, some quite small, with none exercising a dominating role over the others. Among the other three peoples the office of “elder” (kabīr) was normally filled by the head of one of the associated communities in a national federation. Among the Minaeans, however, the kabīr was a biennially appointed magistrate controlling one of the trading settlements or, in some cases, invested with authority in all of them. Legislative functions were exercised by the king acting together with a council and representatives of all the Minaean social classes. Minaean inscriptions make no mention of wars undertaken by the king or the state; this suggests that Maʿīn may have enjoyed covenants of safe-conduct with their neighbours along the trade routes.

Perhaps not the best source but it is quite informative, note the part talking about how none of their inscriptions mention wars conducted by the state of ruler. I would agree that the Minaeans should not be in EBII.
Some stuff on the Hadramaut and Qataban from the same article.

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Inscriptions from the Hadramite kingdom are scantier in number than from the Sabaean, Minaean, or Qatabānian. Yet the Hadramite was probably the wealthiest of them all. Hadhramaut and the Saʾkal area to the east (modern Dhofar province of the sultanate of Oman) are the only places in Arabia where climatic conditions make production of frankincense possible, and Pliny wrote that the whole of the produce was collected at the Hadramite capital, Shabwah, on the eastern fringe of the Ṣayhad sands, and taxed there before being handed over to the caravans that carried it to the Mediterranean and Mesopotamia. In addition, Hadhramaut was an entrepôt for Indian goods brought by sea and then forwarded by land. The caravan trade may have suffered to some degree from competition by Red Sea shipping, which, from the 1st century ad, began to sail through the Bab El-Mandeb Strait into the Indian Ocean. Nevertheless, as late as about ad 230 a king of Hadhramaut received missions from India and Palmyra (Tadmor), at the opposite ends of the long-standing trade route along which Hadhramaut occupied a central position. At Shabwah, French archaeological work begun in 1975 adjacent to the visible temple ruin has revealed a walled town of larger extent than any other ancient Yemeni site. The palace, on the opposite side of the town from the temple, was, according to the archaeological evidence, a truly magnificent building. The main port of Hadhramaut was at Cane on the bay of Biʾr ʿAlī; and the Hadramites had a settlement at Samhar-m (now Khawr Rawrī) on Qamar Bay in the Saʾkal region, founded about the turn of the Christian era.

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The heartland of the Qatabān people was Wadi Bayḥān, with the capital, Timnaʿ, at its northern end, and Wadi Ḥarīb, immediately west of Bayḥān. As in the case of Maʿīn, the earliest references are in Sabaean inscriptions; native Qatabānian inscriptions do not seem to antedate the 4th century bc. Timnaʿ was destroyed by fire at a date not easy to fix; pottery evidence has been thought to suggest the 1st century ad, but epigraphy points to a survival of the kingdom at least until the end of the 2nd century. Its fortunes had fluctuated: in the earliest Sabaean phase it was “liberated” by the Sabaeans from Awsānian domination in the above-mentioned defeat of Awsān. At some periods the Qatabānians themselves dominated a federacy similar to the Sabaean one, and at a relatively late date a ruler whom his subjects called “King of Qatabān” styled himself mukarrib of Qatabān. Inasmuch as Eratosthenes says that this people extended to “both seas”—i.e., the Red Sea and the Gulf of Aden—it might be inferred that there was some sort of Qatabānian presence in the southwest corner of the peninsula, an area later ruled by the Ḥimyarites.

Here's the link http://www.britannica.com/EBchecked/...45968/Minaeans, also has a bunch of books suggested for further reading right at the bottom of the article.