He makes several observations about this dialect, e.g. that they say yā bnu m-ʕamm 'o son of the uncle' for yā bnu l-ʕamm with a definite aritlce am- instead of al-.
Other observations have been made over time, and Christian Robin provides an excellent overview in the Encyclopedia of Arabic Language & Linguistics. The little material that we have of Himyaritic, has been compared with examples of writing in the South Arabian script, which share at least some features with Himyaritic as it is described by the classical Arabic authors, such as a preposed definite article han- rather than a post-posed definite article <-n> as found in Ancient South Arabian proper. These (largely unintelligble) texts in South Arabian script have, rather unfortunately, also een called Himyaritic, while a connection between the two is far from proven.
What is, however, rather conspicuously missing in many of the discussions of Islamic Himyaritic, is a comparison with the modern dialects of Yemen. While many of the features mentioned by the classical Arabic scholars are surprisingly different from mainstream Arabic, they are really not all that different from the Yemeni Arabic dialects as they are spoken today. It seems to me, much more fruitful to compare Himyaritic to modern Yemeni dialects, than to the Pre-Islamic Himyaritic. If we take for example the famous sentence
رايك بنحلم كولدك ابنا من طيب
<rʔyk bnḥlm kwldk ʔbnʔ mn ṭyb>
"I saw in a (lit. the) dream that I gave birth to a son of gold"
We notice several features that are different from most of dialectal Arabic:
First, we see that the 1sg. perfect marker is <-k>. This is atypical for Arabic, while it is attested in Ancient South Arabian, Modern South Arabian and Ethio-Semitic.
However, although certainly atypical for Arabic dialects. 1sg/2sg marking with <-k> is widespread in Yemen (Behnstedt 1985: 116-117).
The second clear feature is the definite article with -n- instead of al-, il- etc. While the definite article il- (that assimilates to the following coronal consonant) is widespread in the complete Arabic dialect Area, the definite article has a massive amount of variation in Yemeni Arabic an-, in-, am-, aC-, iC- (with complete assimilation of the consonant, usually in dialects that have nC > CC assimilation) pointing to *an- (Behnstedt 1985: 64; Behnstedt 1987: map 27).
The indefinite accusative marked with <ʔ>, presumably abnā or ibnā (but perhaps ibnan) is very similar to Classical Arabic, and case is something that is no longer present in the Yemeni dialects. We do, however, have evidence for the old sequence of the nominative indefinite -un yielded -ū in many Yemeni dialects. Dialects that have -ū as an ending for indefinite nouns are found all across the Tihama (Behnstedt 1985: 60). It is of course not difficult to imagine a situation before the loss of case distinction where a Yemeni dialects had baytū, baytī, baytā for the three cases. This Himyaritic sentence could then be considered an example of such a stage. It is however also possible that this vowel is simply a classicism.
A final features it the unusual lexical item ṭīb 'gold'. In the Yemeni dialects ṭīb only ever seems to mean 'goodness', and not gold (Behnstedt 1996: 793-794). However in Ancient South Arabian the meaning of the word <ṭyb> seems to be unknown, and perhaps means 'incense', but certainly not 'gold' (Beeston et al. 1982: 154), so it is not like this is an isogloss with South Arabian over Arabic.
Other features that do not show up in this example, but are mentioned by other classical Arabic authors are, e.g. daw as a negator rather than mā or lā: While not very widespread, dawʔ, daʔ duwwayy are all found as forms of 'no' in Yemen (Behnstedt 1985: 170). This is a feature shared with South Arabian, which has <dʔ> for negation (Beston et al. 1982: 34).
Another oft-mentioned feature is the difference in meaning of the verb waṯaba 'to jump', told within a tragic story where a soldier jumps out of a window, while he was supposed to stand up/remain standing still by the command uttered by a Himyarite: ṯib! Also this change in meaning is attested in Yemeni iṯib 'stay, wait!'; wāṯib 'remaining in place' (Behnstedt 2006: 1281).
Another feature mentioned is the relativizer ḏī over allaḏī, this is once again well-attested in Yemeni Arabic (besides a much more widely attested allaḏī, which is quite rare for modern Arabic dialects) (Behnstedt 1985: 65).
Finally Robin mentions a few more lexical isoglosses, some of these are attested in Yemeni Arabic, while others are found in Ancient South Arabian:
halla 'to be': hall + Pron. suff. 'to be, exist' (Behnstedt 2006: 1264).
bahala 'to say': Not attested in that meaning, but fairly closely related: bahal/yibhil 'to say welcome to someone' (Behnstedt 1992: 115). No similar words in Ancient South Arabian.
ʔasiya 'to find': ʔasa/yaʔsī 'to find' (Behnstedt 1992: 23)
šaʔama 'to buy': Ancient South Arabian <s²ʔm> 'buy, purchase' (Beeston et al. 1982: 130)
ʔawwala 'to bring': Ancient South Arabian <ʔwl> 'to get, obtain; bring back' (Beeston et al. 1982: 10).
ṯaw 'until': Ancient South Arabian <ṯw> (Beeston et al. 1982: 151)
ḥinǧ 'as': Ancient South Arabian <ḥg, ḥng> 'as, according to' (Beeston et al 1982: 69)
Wrapping it up
So was Himyaritic a South Arabian language or was it Arabic? None of the linguistic features that are mentioned by the classical Arabic authors are very strong indicators of South Arabianness, as they are equally present in the modern Yemeni dialects. So the one example of a clear "Himyaritic" sentence, is almost exactly what one would expect 10th century Yemeni Arabic to have looked like. By that definition, Yemeni Arabic is simply Himyaritic. Himyaritic in this definition can hardly be considered anything other than a dialect of Arabic. While many forms of Yemeni Arabic look incredibly exotic, all of them seem to have all the defining innovations that can be used as diagnostic of Arabic (fī as a preposition; mafʕūl passive participle; merger of Proto-Semitic *s¹ and *s³; spread of -at feminine over -t etc.).
When we get to the lexical isoglosses, we are presented with ain interesting problem. Some items are attested both in Yemeni Arabic and South Arabian, and may very well be South Arabian influence on Yemeni Arabic. (e.g. the negative da(w)̣ʔ) . But since South Arabian had this influence on Yemeni Arabic, it does not make Himyaritic any less Yemeni Arabic-like. Some other lexical items that are define by the Arab grammarians as typical for Himyaritic, are attested in the modern Yemeni Arabic dialects to the exclusion of South Arabian, and some of the others are attested in South Arabian to the exclusion of Yemeni Arabic.
In those cases we have to wonder whether we can trust the implicit assumption of modern scholars that Himyaritic is a single language unit. The Arab grammarians were interested in describing correct usage of language of Classical Arabic. It is quite clear that Himyaritic (and by extension Yemeni Arabic) did not fall in the category of 'correct usage'. Within this context, it is of course not surprising that anything that is "wrong" and from Yemen might be denoted as Himyaritic. This would then include both varieties of Yemeni Arabic and some surviving vestiges of Ancient South Arabian. I would be very interested to hear from anyone who reads this and knows more about Modern South Arabian, if any of these lexical items show up in those languages.
So, to conclude: Most of the lexical and grammatical material that is defined as Himyaritic simply appears to be accounts of early Yemeni Arabic (which simply has undergone quite a lot of South Arabian influence). There are a few lexical items that are actually South Arabian, it is of course possible that those lexical items have fallen out of use in the Modern forms of Yemeni Arabic, but were previously in use, but it might also suggest that some of what the Classical Arabic authors called "Himyaritic" was in fact a very late offshoot of Ancient South Arabian.