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While light on a stick might seem like a convenient solution for getting the light off camera the goal isn't just creating shadows and the illusion of 3D but controlling the pattern so it models faces and objects in a natural flattering way.
For starters, moving a single flash off axis is problematically because without a source for fill the flash will created dark shadows where it does not hit. So you wind up trading one problem (flat lighting) for another (dark unflattering shadows). The better solution is to keep one flash near the camera axis for fill (which ideally should be flat and shadowless) while moving a second flash off camera. The master/slave flash systems sold by Canon and Nikon are designed to do that by default by virtue of the master flash in the hot shoe serving as fill in the dual flash lighting ratio.
Secondly, a pole held by the photographer may not put the light at a flattering angle to the faces. Do you understand what factors in lighting flatter faces?
If you start from the baseline of a flash in the hot shoe with a full face subject the lighting is nearly shadowless and the highlights it creates look fake because they fall unnaturally low on the cheeks.
From that starting point one of the simplest ways to make the lighting on the face more natural and more flattering (because its more flattering when mimicking natural angles) is to raise the flash straight up. Keep it centered but raise it so it is above the subject's head. That's what is done to create the "butterfly / Paramount" pattern frequently used for full face glamour and fashion shots.
How high to raise it? High enough to create the same modeling seen in natural light, but not so high that the brow will shade it from the eyes. The ideal vertical angle varies with the person's eye socket shape but usually winds up being between 30° and 45° is average. Lower than 30° and the shadow clues are lost and the highlight clues creep down too low on the cheekbones and don't look "right" per what is expected. What is expected? The more downward modeling of natural light creating downward slanting shadows and highlights on the top of cheeks, lips, chin, etc.
If you also raise the POV of the camera above the eyes so the nostrils are hidden from view you may not even see the shadow the nose casts with the centered strategy. That's one of the reasons it's used in glamor and fashion. If you don't see a shadow hanging off the nose you aren't creating any clue about the shape of the nose in the 2D rendering of the face. That in turn tends to draw more attention to the eyes and mouth. In that sense the nose shadow is an unwanted distraction.
Next take the light that has been keep centered and raised so it hits at a 45° angle and start moving it around the face in an arc. As the key light moves off center the nose shadow that as been hiding under the nose starts to hang out creating what is called a "loop" pattern. This pattern is frequently seen in classic paintings which were lit by studios with high windows or skylights and has been copied in photographs for centuries. It's one of the "classic" lighting patterns. But compared to the centered pattern it changes the over all modeling of the face very little, doesn't model the nose accurately, and creates a distracting shadow on the otherwise highlighted face.
Keep moving the light around the face and the nose shadow moves the opposite direction like a sundial. When the light gets around to the side about 45° from the center of the nose and 45° higher than the eye line you'll see that the nose shadow will move and fall almost exactly over 1/2 the nose on the far side from the key light, overlapping it but not hanging out sideways or down much if at all. That the key light does in that position is model the 3D shape of the nose accurately in the 2D rendering seen in the photo. The key light in that position also will only hit the front side of the cheekbones creating a "mask" pattern of highlights on the high parts of the forehead, cheeks and chin that the brain associated immediately with "face" when seeing a photo.
Now continue to move the light around past 45° from the nose. The nose shadow, which was modeling the shape of the nose perfectly at 45°/45° will now start to hang out sideways from the nose and the nose and depending on it's shape the shadow may fall into the far side eye. The triangle of highlight on the far side gets smaller to the point where all that remains highlighted is the area around the eye. That's the classic "Rembrandt" pattern that is widely copied in photographs. It's very effective for creating a thoughtful, moody, grumpy vibe in a photo of your 80 year-old grandpa, but not the most flattering choice for the wife, kids or grandma.
Move the light even further to the side so it's 90° from nose and camera and the pattern splits the face in half, a classic metaphor for a split personality. Again an effective pattern in some situations but probably not if the subject is facing the camera and smiling and your goal is showing them in the most flattering light.
All of those scenarios are with a full face view. If the face is turned obliquely to the camera to get lighting like this on a face in a candid shot:
The off camera light needs to be placed 45°/45° from the nose and winds up 90° relative to the lens axis:
That's the problem with the light on a pole idea. Yes you can move the light off axis that way, but to move the light off axis and create a flattering 3D rendering of the face with it you'd either need a very long pole, or an assistant who understands how to light a face from their POV on the side to hold it.
I learned lighting 40 years ago by doing that. When I was 20 I answered a newspaper ad and got a job assisting Monte Zucker, who popularized dual flash use for wedding. I started by tending his off camera flash and he taught me where to place it to create flattering lighting and how to see it from off to the side holding the OCF. It's actually quite easy. Stand behind the light and use the stand like the front sight of a gun. Move around until you see the subject's face obliquely with both eyes visible, not hidden by the nose. What is seen is what the OCF will highlight.
But to get a flattering pattern the OCF to the side must be placed precisely, otherwise the shadows don't model the face in the most flattering way. When it's not possible to precisely aim a light from the side at a face because it is moving unpredictably the more flattering strategy when shooting candids is to slide the OCF around behind and use it as rim lighting, relying on the modeling created by the frontal "fill" flash on the camera bracket.
It's not so much that the light on the pole can't work, but one of there being better options if your goal is making the lighting as flattering as possible in as many situations as possible while shooting single-handedly.
Zucker solved the technical problem of recording detail in a brides dress and groom's tux at the same time by using key:fill lighting ratio to fit the scene range to the film with dual flash. The same technique and lighting ratios are needed to record a full range of tone with digital. Yes it is more convenient to shoot with one flash, but one flash will not allow the camera to record detail everywhere.
Zucker solved the logistical problem of shooting single-handedly with dual flash by keeping the fill on a flash bracket over the camera — which also produces flattering lighting in single flash and backlit shots — and putting the OCF on a wheeled stand. Not a conventional light stand, a medical IV stand which is compact but stable.
A few years ago browsing at a thrift store I found a used IV pole for $5 that was made out of aluminum with folding legs. It's called a "Pitch It Sr." because it's designed for single use and disposal. You can see it in the wide shot above. It required a slight modification to allow my umbrella bracket to fit over the top, but its what I now use when shooting candids on location single handed. It folds to 3' and extended puts the center of the flash at 7'
Indoors I just move it around with my free hand. It has five legs in a pentagram pattern making it tip resistant: it just rolls out of the way if bumped.
As noted above more often than not when shooting candids I roll it around back somewhere out of the way and use it as rim light. But that's because I like precise lighting patterns and facial angles. If those don't matter much to you then the light on a pole, aimed randomly, may work better for you. As they say YMMV. I can only suggest what I learned from a very successful pro wedding shooter I've found works quite well every since.