Hans.schenk has done a great job describing the North Gully. My additions are supplements to his catalog of info.
The South Side of the peak is deserving of attention from curious climbers and offers some unique rewards. I wanted to explore the options for an East Ridge route and in the event I could not find an obvious and moderate line that I could accomplish by myself, I intended to circumnavigate further around to the south side of the peak to seek out a weakness that would allow access to the summit. Low and behold, finding the South Gully revealed an easier, albeit longer line to the top. After summitting, I was curious about the North Gully and so I set out to traverse the mountain, south to north. In so doing, I learned a lot about the comparative advantages of these two gullies.
One invitation first: The east side of the peak has a tremendous wall of steep and mostly solid rock. There is a chimney that breaks the wall and I suspect it could be surmounted at a moderate grade for the bold local team willing to: 1) tolerate some grunge on lower sections of class 4 and 2) string out some long sections with little pro. There are not many cracks but the quality of the rock is surprisingly solid.
That said, two considerations should be made by scramblers looking for their easy line to the top. Weather in the two gullies can be entirely different. The South side may be inappropriate for a hot sunny day in April or October but could also offer rewards on the crisp day in January. I ascended on the second day of the year and found the conditions in the South Gully more comfortable than those found in the North Gully. Secondly, The South Gully is technically easier and the route-finding is simpler. That said, one has to travel a greater distance to get there. If you take the view that the greater the distance traveled, the greater the reward, then the South Gully may be your cup of tea. On my way up to the ridge that accesses the S. Gully, I had a good, long look at a herd of 11 Desert Bighorn Sheep that showed me the way to the top of the ridge. Once one is looking up the South Gully, one will feel confident even though the actual summit is still out of view to the right
There is a 'jeep' road that leads to the base of the NE base of the peak. It is useful for walking in or camping along its length (perhaps 1 mile). The turnoff for this approach road can be easily found along Silverbell Rd. about 100 yards west of a cattle guard. Secondly, I refer to this as a jeep road. I drive an all-wheel-drive with very little clearance (Subaru Legacy) and it managed this approach road. It depends on what you are comfortable driving.
Head for the saddle to the east of Ragged Top. Skirt the peak until you can look up the South Gully.
Sonoran Desert garb is appropriate. The flora is out to rip you and make you bleed. Protect yourself and your budget. Leave the tech gear in the car. Loose-fitting Carhartts and other tough cottons are the textiles of choice. Gloves are also helpful.