game4lunch

Start with good optics. Spotting scope is almost a necesity.
Getting close is the whole hunt! You can put together the best plan, and as soon as you crest that hill through the cactus on your belly, the herd is topping the NEXT ridge! They have Cheetah speed, and 8 power vision.
First thing you do, practice 200+ yard shots. A LOT! Know your balistics. Antelope go down pretty easy. 7Mag is big for Antelope for instance. But works well.
If you have time to scope an area enough to know their dailyt habits (eating and drinking), use that info to set up and "cut 'em off". No matter what, be prepared to make a long shot.
PRACTICE . . .PRACTICE . . .PRACTICE! I say this not just as an avid goat hunter, but experienced guide as well.
Here in Wyoming, the rut starts in September, so I would guess it to be the same in NW NM. Probably will be pre rut. Antelope and sociable animals. They are always together. They aren't like other species that group up in bachelor or doe/cow groups. Bucks will be with the herd all year long.
Remember, your best weapon is confidence in the long shot.
One last thing, skin it out, cool it off right after harvest. Excellent meat if you care for it. If you tie it to your hood back to Texas, you'll have 57 pounds of Jerky.