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My starting baseline with flash was having the top wedding pro of the day (early 70s) hand me a Rolleiflex with single power manual flash above it on the custom bracket and an identical flash on a rolling stand, which I later realized was a IV pole not a light stand. He said "Use this, it works" and proceeded to show me how and why.
Raising a single flash straight up makes single flash shots more flattering than flash on camera by: 1) hiding most of the unfilled shadows, and 2) making the vector of the modeling a closer match to the downward vector of natural light. That's not how Zucker explained it, he just stressed the importance of getting light in the eyes and avoiding harsh shadows if you want to flatter the subjects in single flash candid shots.
Zucker also understood (before many of his contemporaries) that when a single flash is moved off axis it creates UNFILLED shadows that are dark and unflattering. The solution for that used in studio lighting is to keep a second fill source over the camera. That's what the flash on the bracket becomes when a second light is added IN FRONT OF THE FACE. Why do I stress the back of the face? Because when the off camera flash is behind the subject, it's like natural backlighting by the sun and whatever you use on the front side needs to provide KEY and FILL on the face, or alternately hide the shadows as with a single flash and a bracket.
So given that equipment; a flash on a the bracket and one on a stand there are two flattering strategies for people photos:
1) When you can't precisely align the face to OCF don't put it in front of the face. If a light is in front to one side and the faces are moving half the time the face will be turned away in shadows. If there isn't a ceiling bouncing "spill fill" back into the shadows they will be dark and unflattering. Remember flattering the subject is the goal of the exercise here.
When faces are moving around, in candids or in a studio session more flattering results overall are obtained by keeping the "Key" modeling source centered and overhead: what the bracket does in automatic "no brainer" fashion. Thus a more flattering strategy is bracketed flash in front to model the face (as in the single flash shot) with OCF behind acting not as "Key" but as "Rim" lighting to define the overall shape of the person, add a sense of 3D space a front>back lit shot lacks, and more evenly light the background behind the subject.
Logistically working with two flashes that way is as easy as one. Just park it in a corner behind the action and keep it out of the frame. For more background ambience bounce it off the ceiling. For more of a "stage lighting" look with a darker background to isolate the foreground action use it direct.
2) If you observe any "candid" situation you will notice where people turn and look when talking to someone or looking at the action it the room. At a wedding there are a lot of traditional staged events like toasts, cake cutting, etc. which are also predictable or can be manipulated by the photographer to get flattering "studio style" results. By studio style I mean careful attention to light placement on the faces and camera angles. What made Zucker famous was his attention to those details in the candid wedding shots.
It's not really difficult as he explained it. Take the OCF and put it so it is 45 degrees from the subject's nose and over their head REGARDLESS OF WHERE THE NOSE IS POINTING. Then walk around to the front or the other oblique view and take the shot. In other words, don't think about where the OCF stand is on the floor relative to the camera (as seen in all those lighting diagrams you can download) focus on where the light is RELATIVE TO THE FACE.
Once you grasp the difference intellectually lighting a face is much simpler to understand. In a candid situation where the person is moving around I will set the OCF to put it 45 degrees from where the nose points most of the time, walk around until I'm 45 or 90 degrees from the OCF and wait for them to turn full face (when 45 from the light) or obliquely (when 90 from the light) to my camera. If I move around to where I'm 135 degrees from the light I can capture a dramatic profile.
Back in the day shooting weddings I'd try to capture the best man toasting all three ways. I'd start 45 from the OCF for a full face / full length wide shot as looked at the couple (predictably) and started his toast . Then with the light hitting the face from the same 45 degree angle RELATIVE TO HIS FACE I'd move the camera around until I was seeing his face obliquely and tighten the crop to H&S. Then if the toast was a long one I'd move around until I was looking at his face in a perfect profile and wait for the "decisive moment" when he lifted the glass high. Same lighting relative to the face, different POV for the camera selected to look balanced, natural and flattering in the photo.
It's really that simple to get "studio style" lighting in candids with dual flash. It that the only way to use two flashes? No of course not and I'd encourage you to try them all. But I'd also give you the same advice Zucker gave to me 40 years ago: use this it works
It will work with whatever flashes you choose or however you choose to trigger them. Adding modifiers will change the character of the lighting but the MODELING the light creates is a function of where the key light is RELATIVE TO THE FACE. If there is more than one face in the photo (couples / groups) it's simpler to get flattering results "on the fly" with centered lighting (i.e. move the OCF behind as rim light and rely on the flash on bracket to model the faces).
If you decide using a bracket is too much of a hassle your direct lighting vectors on the face will be unnaturally low, even with a diffuser. Will bouncing solve that problem? Only if there is a ceiling. The better approach? Use a bracket + diffuser + bouncing when possible and the bracket and diffuser when bouncing isn't possible.
Should you use the built in flash as Master (if your camera has that feature)? Yes it will fire the slave and work as fill in some situations but will be too low to the faces when you move the OCF behind. When using a Master controller it will also lack the range of a Master 580ex flash.
When buying into the Canon system in 2004 I opted for a pair of 580ex flashes. If I was on a budget today I'd do the same. The 580exII is newer, but it has several design related problems such as random firing at full power in TTL (film body mode) it also lacks the Master/Slave switch on the base which is very convenient when shooting on the fly and needing to take a few shots without the Slave.
If budget allowed and need justified I'd buy a pair of 600EX-RTs. I'd skip the ST-E3 as I did the ST-E2 because the Master on bracket has more advantages that wrangling two stands in situations were I'd use speedlights vs. my studio lights. I haven't upgraded to 600EX personally because I've never had a problem with the optical signaling and don't a need for the other features.
Again, my approach with speedlights is one of many and based largely on the fact I started with two on bracket and stand in the beginning. I've tried just about everything else since myself and still find it the best solution for what I shoot with speedlights. Try it, then try everything else and decide what works best for your needs