The route you want to search for is called "
El Camino Del Diablo", and it is supposed to be really interesting and incredibly remote. I have not done the route yet, it's at the top of my TO DO list though, and I hope to do it come January or February. It's typically a three day trip if you go end to end, and you will need to be 100% self supported, there is no food, gas, or water stops on the route. There's
a great write up on Expedition Portal and a nice
video series and writeup by AZ Offroad. If you are interested in doing the full route, there is a permit required, as you pass through a wildlife refuge and a LIVE bombing range. I believe you will also need to sign in with close to exact times and locations of when you will pass through the bombing range - you know, so you don't get blown up. If you are only interested in the eastern section where it cuts through Organ Pipe, I think you'll be fine without the permit, but do a bit of research to make sure.
I believe
@1Louder and
@Gunnermoose have done the route so they may have more specific information