First, I will not misrepresent me experience, as I have only one Coues deer (that's the variety of whitetail you will be pursuing) to my credit. Using the techniques I describe, we almost always flush does, so the basic concept is valid in my opinion. I have not hunted in 33, but have hunted Javelina on the other side of the San Pedro in 32. I hunt deer in 36B, but I think once you survey the terrain you'll feel my comments are valid.
There are very few nice round hills or mountains in Southern Arizona, and they are not heavily wooded (unless you're near Mount Lemmon?). The norm is very steep, horizontal, and often parallel ridgelines. Northern slopes tend to have more vegetation than the southern slopes. Very rocky, with a lot of cacti on the lower elevations, offering pretty decent long range observation. Early morning/late afternoon tactics should have you on the high ground, scoping out as much terrain as possible. My buddy and I often see movement this way, but planning a stalk in a timely manner is difficult, because they are several hundred yards away, and the terrain is difficult and relatively open.
When they movement stops is when you want to start your driving. Here is where I think you'll find it is not practical for one man to stay in one location. You just can't see most of the possible turf the deer may be moving to. We usually have one of us go low, and the other parallel his movement higher up on a ridgline. That way either one of us has a chance to see what the other may flush. Where ridglines are close together, we might walk parallel ridgelines, and have the advantage of looking into the compartments on both sides.
The "beater" should work draws or reentrants between slopes, as they are more vegetated and deer often bed down in them. When the draw levels off, becomes more sandy, and your in what is more properly a wash, stop and do something else. These deer like to stay high, and don't spend a lot of time in true washes. We usually walk into the wind. Art's comments on the downwind side of the slope, with being able to smell what he can't see on the otherside, are right on.
They don't run far. Typically, you'll flush one at a distance too long for a shot, and they'll make a bee-line for the other side of the ridge. Once on the other side, however, they'll usually turn and parallel the ridgeline, preferring to stay high. They'll also slow down, and resume a leisurely pace shortly after cresting the ridge. Here is where you play the guessing game of "did they zig or did they zag?". You'll have to survey the lay of the land, with precious little concealment, and plan your next move quickly yet carefully. This is what makes hunting these deer the great challenge that it is.
If you do end up close to Mount Lemmon, or terrain not like the high-altitude desert I described, then what I have to say might not apply that much, but most of the time it fits the bill. The important thing is to adapt your two-man tactics to what you see on the ground, and not just the sage advice you might get here or elsewhere.
Perhaps the best advice I can give is to take the lessons of those whose experience is limited to the Eastern Whitetail with a grain of salt. Absolutely no disrespect to any of my fellow TLFers, and especially those with more bucks under their belt (which is almost everbody!) But the fact is most people looking at the place where I hunt can hardly imagine there is ANYTHING fuzzy living out there, let alone deer! The pursuit of the Coues deer of Southern Arizona is a very unique hunting experience.