I do not know the height of the tank in question. I currently keep my BTS, Frank, in a 5X2'. He is moving, as are all my animals, to a 6X2' boaphile tank (Jeff Ronne is making a 5 tank apartment complex for all my reptiles). The tank I am having made for Frank is 17.5" high, so I can put both a small basking light and a UVB bulb.
First, Skinks like to explore and move around. I have read that the bigger the ground area, the better. Having said that, a 4X2' should be fine.
Secondly, BTS do need UVB exposure and like to bask. I have an UTH and Frank still likes to sit under the UVB and basking light.
In the new tank, I will have UTH and a radiant heat panel to maintain 90ish on the hot side, with a 94-97F hot spot under the small basking bulb and fluorescent UVB bulb.
I am probably not telling you anything you do not know, but wanted to be clear on the UVB requirements. I have had trouble finding a lot of good info on BTS and wanted to make sure you knew.
All the best.
David