Well, seeing as how there is a lack of care information on these guys in general, (Wild and captivity) I've decided to take it upon myself to share information I've learned after seeing these animals in the wild and learning their natural behavior. 

Most of the "common" (Being a relative term, with all the war and drama circulating the region now it's hard to find any Middle-eastern species for sale anywhere) Middle-eastern agamids are likely to be in four genuses, Pseudotrapelus, (Sinai agama and relatives) Trapelus, (Most common species that wind up in the pet trade, frequently misidentified as the Sinai agama, thus leading to improper care) Stellagama, (Starred/Painted/Clown agama, there are already many good care sheets on this species, but they come into play later into the article) and Phrynocephalus (Toad-headed agamas, I won't go into detail of the care of all the 44 species of toad-heads, it will mainly be the Arabian toad-headed agama, but I think that several species of agamid, not just other members of Phrynocephalus will need the same amount of care as well)

To start with, proper identification is key. most "Sinai agamas" in the pet trade are largely mis-identified species of Trapelus, the most likely candidate is probably T.lessonae, which has the horizontal stripes I've seen on most of the mystery agamas on this website and others, along with keeled scales, and ears smaller than the eyes. A key to identify the Sinai agama from the other agamids in the region it the ears being the same size or slightly larger than their eyes, long, spidery legs, and relatively long tail in comparison with the body. (Tail almost always longer than the body) To make even more confusion, there are now multiple species in the genus Pseudotrapelus! If the import list/localities came from the Red sea region (Aqaba, for instance, areas of Egypt, possibly Saudi Arabia, and possibly Israel) might be P.aqabensis, a new species described from DNA evidence from the Aqaba region, and believed to be limited to the rocky cliff-faces surrounding the Red sea. If the localities come from Oman, they could either be P.jensvindumi or P.dhofarensis, which come from North-eastern Oman and South Oman respectively. And if from Sudan, (And probably the surrounding region) could very well be P.chlodnickii. And hailing from the southern areas of Saudi Arabia and Yemen are likely going to be P.neumanni. Nearly all of which are distinguished from P.sinaitus from the 3rd rear toe being longer than the 4th rear toe, and P.neumanni, which has no toe identification, can be distinguished from P.sinaitus and other members of Pseudotrapelus, from large scales on the top sections of the head and body. All of which have the same care as P.sinaitus though, aside from identifying it from another Pseudotrapelus or Trapelus species you can keep them the same way as P.sinaitus.

Identifying the Trapelus species seems to be more difficult, as several species ranges overlap and look similar. The most common seems to be T.lessonae, as it has dark bands on its body, keeled scales, and ears smaller than its eyes, and the males have just enough blue on their throats in the breeding season to be mistaken for a male P.sinaitus. Another common species might be T.mutabilis/pallidus, which has undergone major amounts of taxonomic revisions over the years, especially the pallidus subspecies, which for the longest time has been thought to be its own species from the Desert agama/T.mutabilis. (T.pallidus, Pale agama) It is now thought to just be a subspecies of T.mutabilis, and should be treated in captivity as such. One last species that might wind up into the pet-trade might be T.savignii, the only reason I say might is because of this species comparatively small range, and the ban of exportation of reptiles from Israel, (At least I think its illegal to export animals from there) and the lack of exports from the rest of its range. (Egypt and small areas of Palestine) most, if not all of the other members of this genus have the exact same care as will be listed, as I will not be going into details of all the other species in the genus.

Phrynocephalus arabicus, the Arabian toad-head agama hasn't had much going on, in terms of taxonomic revisions, or exports in general. Even though there isn't much to say on the genetic relations of this species, its unlikely not going to be mistaken with any other species, unless other Phrynocephalus species are exported along with it.

To begin with the actual care of these animals, of course you need to do your research on the actual niches that these animal inhabit in nature. The many species of Pseudotrapelus, (And Stellagama for that matter) always are found on cliff-sides and hard, boulder-covered mountain sides, and boulder-strewn areas in nature, using them as look-out points for mates, rivals, food, and predators, and natural camouflage. (When you compare the normal drab gray-brown colors of both males and females in nature with the habitat and boulders they live in, you will see what I mean) They spend a large portion of their day basking in the sun on the aforementioned boulders, and when the heat of the day becomes too warm for them, they seek shelter either in burrows, underneath plants in the shade, or move to naturally darker areas. For instance, an area close-by to where I live, (Wadi Rum) typically gets up to 30 degrees Celsius, but has been frequently reported to get to 40 degrees Celsius or more, showing the type of environment they live in. There doesn't seem to be a lot of information on the diet of these lizards, only that, despite their relatively large size, (18cm) they primarily eat ants. This seems to be mainly because ants are the most common insect they can come across, because they also have been recorded eating different types of locust, and likely would eat crickets, and other arthropods and small vertebrates. (They likely would eat other small lizards, snakes, and mammals) Before I go into depth on the care of this species, if you really need quick care tips, keep them generally like a much hotter and drier Starred agama enclosure, (I told you they'd come in later into the article ) with very strong, powerful UVB.

The different types of Trapelus, in general inhabit different ecotypes and niches, depending on the species you have, or plan to get. For instance, T.lessonae, the most commonly mis-identified species of Trapelus in the trade, does NOT live in extreme deserts, like the Sinai agama it is being mistaken for, which as you can imagine, would not lead to long lives with species already on the brink due to (Probably) bad conditions right after being caught, bad conditions once shipped, and all the diseases they might have picked up from all the stress and improper care. This species, in the wild, lives in rocky semi-arid areas, (Of course not the same as an extreme desert, where the Sinai's and other members in the genus live) and steppe habitats. According to a credible source, it does not climb rocks and trees regularly, except possibly to bask in the cooler, early morning sections of the day. Despite my best efforts, I can not find any links or articles about the diet of this species, feeding somewhat small live-food is probably recommended. T.mutabilis is generally what you'd expect of an agamid from this region. It lives in semi-deserts to habitats as harsh as extreme deserts, like areas of the Sahara in Northern Africa. It tends to inhabit stony, gravely plains, devoid of a lot of plant cover. (Of course a lot of desert plants in the enclosure would benefit the animal, as basking sites and shady hiding places) It is a sit-and wait hunter, eating anything small enough for it to eat, relying on its cryptic coloration to aid in hunting and hiding from predators. Once again, like the Sinai agama, its main prey consists of ants, but once again, seems to be mainly out of convenience. They have been recorded eating caterpillars, beetles, and when the opportunity arises itself, migratory (And non-migratory) locusts. Once prey is spotted they quickly run twards the animal, and grab it with their mouths. They have been documented jumping as high as 10cm to grab flying prey above them. Interesting to note, this species has been recorded to "Rain-harvest," which is a type of water-finding method desert animal frequently use in the early morning, when dew can condense. They lift their rear-ends into the air, and channel water from their bodies to their mouths, helping them in the heat of the later portions of the day. T.savignii is also one of the stereotypical members of the genus. Naturally occurring in sandy and gravely desert habitats from the Negev to the Sinai region in Egypt, its unlikely to wind up in the pet trade, simply due to the small range of the species and the laws restricting the animals there. Since there is a lack of information on this species, it seems like your best bet would be to care for them in a similar manner to T.mutabilis, and see how well they do from there. All of these species need intense UVB lighting, to replicate the deserts and semi-deserts they naturally occur from. Just as long as you provide large enclosures with room to thermoregulate, they should be fine.