The gate to Thompson Canyon's southern end is locked and is no longer a viable option for short and convenient access. The standard access is now via the longer, rougher Davenport Lookout/Thompson Canyon route.
New Mexico CRAG (NMCRAG) will continue to be in contact with the ranch owners and the Forest Service to see if it can resolve this issue. In the meantime, please respect the closure, spread the word and don't attempt to drive through the private ranch.
Sleeping Beauty Wall is found just up and left of the Enchanted Tower in a sort of squared-out rectangular alcove. The middle section of the wall is overhanging. A pretty good range of routes are located here, from 5.9 to hard 5.11 and from complete jugs like those on Cheshire Cat to tiny crimps on Glass Coffin and Poison Apple. This seems to be a pretty popular area, so likely that you'll have company during the "season".
You can hike up to the Sleeping Beauty Wall from either side via trails along the slopes below the wall.