@Preacher
When my son and I hiked the Black Hills and Tortilla Mountains segments, we cached water. For the Black Hills segment, Sredfield gave me these tracks:
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My wife and I followed the green route to the end, and then followed the red until it crosses the main yellow AZT # 14 - Black Hills trail. That point is very close to the exact middle of the Black Hills segment. We put our Suburban in 4-wheel drive, and drove carefully. Turning around in the wash was nerve wracking, but we did it! Your "2 wheel drive pickup" should be OK. There are lots of YouTube videos on how to drive on sand. Watch, listen, and obey!
For the Tortilla Mountains segment, we cached water here: (Now that I think about it, if I remember correctly,
@Sredfield gave me this track, too!)
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Follow the black route as far as you care to.

My wife and I parked at a small campsite about 2/3rds of a mile in on the right (east) side of the road. From there we walked the rest of the way. Again, 4-wheel drive was our friend, but not really necessary on this stretch. It all depends on how far you drive in. Further in, near the end, there are some HUGE erosion ruts crossing the road. I wouldn't have been able to cross them in the Suburban. Maybe a 4-wheeler or Razor(?)?
There are steel water caching bins(?) boxes(?) containers(?) at the start of the Black Hills and Tortilla Mountain segments, as well as another just before the parking lot where the trail crosses the Florence/Kelvin Highway. Sometimes there's water in them, sometimes not. You take your chances!
The only other semi-reliable water supply is the caching box near the end of the Gila River Canyons segment, and the start of the Alamo Canyon segment. I've never been there, so I can't vouch for its reliability. I've heard that it is jeep accessible. I don't know. Check with the trail stewards. They'll have better information.
Have fun, and be SURE to report back, and let us know how it went!
Pictures are always appreciated!
Gary