The desert mule deer in west Texas aren't like whitetail. Lazy devils. They don't wander around nearly as much, exploring the area. They aren't as agressive about breeding, during the rut. And, generally, most of the rut happens after the season ends. Mostly, you gotta kick Bucky out of bed and decide whether or not he's worth shooting.
Bucky sorta goes on a feeding frenzy in October and November, building ujp a bunch of tallow to carry him through the rut. Anytime the temperature is above freezing, he's not real happy at wearing the equivalent of an arctic parka, so he stays in bed a lot. Cooler that way. You generally find them bedded down just below the downwind crest of a ridge, near a saddle. They'll take off and run upwind and uphill, when spooked.
Sometimes they'll be a bit farther down a slope, snuggled in among some brush.
Not often do you see them in the low country during the day; sometimes, yeah, but not as much. And after a bit of shooting, they head on out for the high ground.
Bucks only drink water maybe a couple of times a week. Does habitually stay within a mile or so of a water point; imprinted, since a lactating doe must stay fairly close to water.
So you have good odds of a quartering-away shot on a running buck at a couple of hundred yards. If you're lucky. You only have seventeen days, and the population of decent, shootable bucks isn't all that great. You pretty much take what you can get, in the way of a shot.
If he's worth shooting, he's gonna dress out somewhere north of 150 pounds, maybe up around 200.
Sure, the .25-06 will kill the heck out a mulie, if everything's going your way on the shot. Me, I'd rather move on up to a tad more bullet for probably-better odds on that quartering-away shot.