There's a number of different ways to approach Browns Canyon from the south, along Hwy 60. There's at least three major jeep trails:
As seen on this map I started on Microwave Relay Rd at 33.800086, -113.18864. The trails split, and join, and eventually converge maybe a mile below Brown's Canyon Dam. 4x4 recommended. If you have the vehicle, the further up you feel comfortable driving, the more time you have to explore Brown's Canyon Wash. Otherwise, from Microwave Relay Rd, it is about a four mile hike to the dam. You don't need a GPS route -- I did not have one -- simply aim for the saddle west of Hill 4489 (the large mountain immediately west of Eagle Eye Rd). If you decide to go cross country, that is not a problem, as the ground is ankle-breaker and thigh-stabber free. The vegetation is mostly creosote and White Bursage, with a few brittlebrush.
About a half mile south of the dam, Brown's Canyon Wash begins tightening up. There's a lot of pools, and around everyone of them are copius piles of poo, mostly of the bovine variety. Drink only after heavy filtration, and even then only if you are desperate. As you work your way north, you will need to negotiate many boulders and rocky out-croppings, both below and above the dam. The dam itself is a small butressed wall of concrete. In dry times, a trickle of water from an underground stream will seep under it.
A half mile northwest of the dam, just before Brown's Canyon proper, is a small triangular plateau that has the largest, greenest, most beautiful ocotillo you could ever hope to lay eyes on. There's a spring near the plateau, though I did not find it.
Somewhere between a quarter and half mile past the plateau, if you look north, up the west slope of Hill 4489, you will see an absolutely amazing field of thousands of saguaro. Somewhere in that stretch, you need to begin bushwhacking your way up to the saddle. It will be much slower going than the first four miles of the hike, not only due to slope, but multiple wash crossings, numerous 2-3 foot rocks that need to be stepped up/around, and more palo verde, catsclaw and cactus than you can shake a hiking stick at. It will be slow going. Because I was hiking without a GPS route, I veered east of the saddle, about 200 feet higher up. From 3000 feet, I could easily see Gladden and the APS substation.
From your high point, work your way north to the prospects, where you can pick up a jeep trail that four miles later will deposit you at the substation. There is a multi-acre corral about halfway between the prospects and the substation. From the corral north to Hwy 60, the road is easily travelled by a city car. If your shuttle driver parks at the corral you will save time for exploring / cut time off your hike.
In summary, Brown's Canyon is well worth the time you spend in it!
Note: The 'official' route is really just a guideline. Regardless of whether you do the hike south-to-north (as I did) or north-to-south, all you need to do is aim for the saddle.
WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.