Yes, they need either a reptisun 5.0 or an Arcadia 6%. The Arcadia’s are good for a year and the reptisun are good for 6 months or a little more then they need replacing. What is a desert light? Is it a uvb? If so the only ones recommended here are the reptisun or Arcadia.
I think most people use the aforementioned Reptisun 5.0 or Arcadia 6%. But it depends on your enclosure and your fixture. I actually use an Arcadia 12% desert bulb for four hours a day and a dying Reptisun 10.0 for the rest with some overlap because I have a quad fixture that loses a ton of my UVB output and my vivarium is super densely planted, and I'm using a UVB meter to check the specific output and that's just what I need for my setup. (That information is not a suggestion so much as to make the point that if you're using uncommon equipment the standard husbandry info you'll find online may not apply).
Presuming you don't have access to a UVB meter and you're using a the "standard" type of setup (mesh repti-breeze or similar enclosure with a single reflector UVB) there's some useful placement information in the aforementioned article that will help you get set up without the UVB meter.
Oh my word, thank you so much for going into so much detail. I really appreciate your effort to enhance the joy of looking after Figaro. I will have him a year next month.