That's about the scariest road I have ever driven, with a very high Pucker Factor -- The first time was when I pulled my overweight Jayco 16' with my old D1150 -- First gear all the way and I had to go on the outside of the right-hand turns, because the insides were too steep, praying that no one was coming down -- I passed a rental car full of tourists overheated on (luckily for me) one of the left-hand turns -- Several times I had to get in the left lane because the right lane's washboarding was making my truck/trailer start to dance towards the edge.
Uphill gravel/dirt road driving tip -- The uphill road usually becomes washboarded or dug out on the normal (right) side first, so the other lane is often more useable.
According to the local guy who assured me I could make it (I was seriously doubting it about halfway up), the road was originally built for uranium ore trucks and he was one of the drivers.
I've been up/down steeper roads in other places (Lincoln Gap VT 14%; Telegraph Creek B.C. 22%), but Moki Dugway is worse because of the switchbacks.
BTW, a really memorable place to camp can be found by taking the gravel road to the left at the top of the hill (about where the pavement resumes) and following it out to the tip of the plateau at Muley Point, which is just inside the Natl Rec Area -- Dry camping
with tremendous views over the Goosenecks of the San Juan River and Monument Valley -- I was lucky enuf to have it to myself and the only lights
I could see in all that space were the airplanes waaay up there.