I would recommend checking out SoCal Herps. They breed Red Eyes Croc Skinks! They have a YouTube channel as well that you can search for their care tutorials as well. I grouped that together with contacting other breeders for care as well as other care sheets I happened to find online.
I keep my single female in a 10 gallon enclosure, that is bio active. I use a 40 watt nano bulb and heat fixture for additional heat. These animals don’t bask and tend to bury into the substrate. Mine mostly hides under the water dish since it’s really humid below. I use an old zoomed reptisun 5.0 linear tube for UV exposure. These animals are crepuscular so they are really only ever active in dusk and dawn. I provide a lot of ground cover with leaves and cork so they feel more secure. I also have put up something on each side of the cage besides one side. This will help make the animal feel a bit more secure. I also have a food dish filled at all times with grub type feeders as they scavenge for food. This dish is covered by a large cork piece that has enough clearance so the skink can access its food. She also eats a lot of isopods that are in the enclosure.
The most important thing I can stress about keeping this species is that you need to make sure there is a clean water dish full of water at all times. I use a plant pot drainage tray, she often lays in the water. Provide a lot of hiding places as well.
I keep my temperatures around 74 degrees and it drops down to about 70 at night.
Also just a forewarning. These animals will sqwuack at you if they’re feeling threatened. I generally access the cage daily to check water and food as well as misting the enclosure twice daily for about 30 seconds to boost humidity. I try to keep it at about 80% but generally it goes down to about 50% with the heating element. Thankfully she can crawl into hides that are more moist as well as having access to the water and digging into the substrate.