I deer hunted 30 3 years ago... BLM near White's City, off dark canyon road. Never saw any sheep but wasn't looking for them either.
The fact that a guy from colo applies for an archery dad tag in SE NM kinda baffles me. The grass is always greener I guess... Well, not in the desert in Jan.
At any rate, gohunt says that 29 is one of the better units for sheep in the state. It also says that you're less likely to see sheep than deer or antelope.
I'd plan a mobile hunt with lots of glassing from high peaks into the rough and broken stuff. By mobile, I mean being prepared to drive to different areas