I use to hunt 24 pretty hard just to the east. Lots of deer around Silver City and over in the Burro Mnts. but that might be excluded from 23, have to check the rules. Drove down the highway one night from Reserve and there were tons of deer feeding on the grass next to the highway. Glad none of them decided to take on the car.
Also if you get a general tag you might run into a Coues whitetail. Some areas down there they separate whitetail and mulie tags so you get one or the other. Some tags are good for any forked antler deer. Good luck on the draw and results are on the web.