Jenkins et al. 2020 review
“the phylogenetic placement of an enigmatic reptile from the Early Triassic Transantarctic Mountains.” This reptile has gone through some name changes, but the large reptile tree (LRT, 1751+ taxa) nested it in 2016 with similar, big-eyed, basal placodonts like Palatodonta and Pappochelys (Fig. 1). Co-authors Jenkins and Lewis (2016) nested it with rhynchocephalians, but limited their taxon list to rhynchocephalians and procolophonids. There is no indication that they included basal placodonts in 2020.
Originally
(Broom 1906) considered what little is known of Palacrodon browni (= Fremouwsaurus geludens; Early Triassic; Fig. 1) a member of the Rhynchocephalia.

Figure 1. A comparison of basal placodonts to scale (and Paraplacodus reduced to one-third shows how Fremouwsaurus (Palacrodon) is transitional between the small spike-tooth ancestors like Palatodonta and Pappochelys and the pavement toothed Paraplacodus.
From the Jenkins et al. 2020 abstract:
“The phylogenetic placement of Palacrodon has been contentious since its initial description, with workers naming it as either a rhynchocephalian, lizard, procolophonid, eosuchian, or archosauromorph.”
Taxon inclusion nests it with basal placodonts.
“The uncertainty surrounding the phylogenetic affinity of Palacrodon in large part stems from the fact that nearly all the specimens found are teeth and fragmentary portions of tooth-bearing bone. Palacrodon bears characteristic labio-lingually elongate, molariform, cuspidate teeth reminiscent of herbivorous reptiles like extinct trilophosaurs and polyglyphanodonts and modern shell-crushing lizards.”
“Because previous workers lacked any other skeletal material, Palacrodon has never been placed within a phylogeny.”
Never? The LRT placed it in 2016,
“Though its phylogenetic affinity is uncertain, Palacrodon is a cosmopolitan genus spanning most of the Triassic, with specimens found in the Early Triassic of Antarctica, Early-Middle Triassic of South Africa, and the Late Triassic of Arizona. The only specimen of Palacrodon possessing more than dentition is from the Early Triassic lower Fremouw Formation of Antarctica (specimen number BP/1/5296). That formation is the sedimentary sequence immediately preceding the Permian-Triassic mass extinction boundary in the Transantarctic Mountains and represents the only known Early Triassic paleopolar deposit with abundant tetrapod material. The Antarctic specimen of Palacrodon was described from the impression of a latex peel as a partial small skull belonging to an unknown diapsid reptile initially named Fremouwsaurus geludens, which was later synonymized with Palacrodon.”
“We CT scanned the Antarctic specimen and found that previously undescribed skeletal elements are preserved in BP/1/5296. These include limb bones, ribs, phalanges, caudal vertebrae, ankle bones, and an ilium. Of the cranial elements, portions of the right maxilla, lacrimal, prefrontal, jugal, postorbital, ectopterygoid, and dentary are preserved. Both parsimony and Bayesian analyses found Palacrodon to be a stem saurian with close affinities to drepanosauromorphs.”
See figure 2 for known drepanosaurs (all Late Triassic) and their ancestor, Jesairosaurus (Early to Middle Triassic) in the LRT.

Figure 3. Drepanosaurs and their ancestor sisters, Jesairosaurus and Palaegama to scale.
From the Jenkins et al. 2020 abstract:
“This finding suggests that Palacrodon is the earliest known drepanosaur, extending the temporal range of the clade by nearly 20 million years. Palacrodon is also the only known drepanosauromorph from the southern hemisphere. Further analysis of these new skeletal elements will now allow a more thorough understanding of the behavior and niche of Palacrodon and primitive drepanosuars generally.”
Excluding far fewer taxa, in the large reptile tree (LRT, 1749+ taxa) moving Palacrodon from the base of the Placodontia to the base of the Drepanosauromorpha adds 8 steps based on very few skull traits. Of course the post-crania could change things, but usually taxon exclusion changes things more.

Figure 2. The head of Palacrodon and the headless body of the Majiashanosaurus compared.
References
Broom R 1906. On a new South African Triassic rhynchocephalian. Transactions of the Philosophical Society of South Africa 16:379-380.
Gow CE 1992. An enigmatic new reptile from the Lower Triassic Fremouw Formation of Antarctica. Palaeontologia Africana 29:21-23.
Gow CE 1999. The Triassic reptile Palacrodon brown Broom, synonymy and a new specimen.
Jenkins K, Lewis P, Choiniere J and Bhullar B-A 2020. The phylogenetic placement of an enigmatic reptile from the Early Triassic Transantarctic Mountains. SVP abstracts 2020.
Jenkins KM and Lewis PJ. 2016. Triassic lepidosaur from southern Gondwana. Abstract from the 2016 meeting of the Society of Vertebrate Paleontology.
Neenan JM, Li C, Rieppel O, Bernardini F, Tuniz C, Muscio G and Scheyer TG 2014. Unique method of tooth replacement in durophagous placodont marine reptiles, with new data on the dentition of Chinese taxa. Journal of Anatomy 224(5):603-613.