Hiya Debbie, I know there have been a lot of helpful answers already but I just wanted to add my input, being an Enigma owner myself
Star (named after her star gazing habits lol) is around 7 months old now and doing well. She will usually Star gaze quite regularly, I often catch her staring up at the vivarium walls or ceiling, her eyes are wide, head tilted, completely fixed on something. Then, quite suddenly, she will snap out of it and return to roaming about her enclosure.
What you have described doesn't sound like Star gazing as you say her eyes are closed.. it almost sounds more like a stretch or even a sign of contentment

I have seen my females arch their heads backwards, close their eyes and look up for short periods, usually just after basking or waking up. Without seeing her do this though, I can really pass accurate judgement.
Just out of interest, have you ever seen her spin (chase her tail) at all? And how is her hunting ability? Does she ever miss her prey?
I am conducting a personal study of Star's behaviour on a daily basis in order to further understand the Enigma Syndrome. Im lucky in that Star is only what I would class as a moderate case. It's a truely upsetting condition to witness sometimes, and despite my devotion.. I dare say had I known prior to purchasing I probably would have avoided her. At the same time though, I cant help wondering that had I not chose her that day, she would now be stuck with a spoiled child who doesn't know a thing about the proper husbandry of Leo's.. let alone the needs of an Enigma!
Do let us know if anymore odd behaviour is seen!