Home Depot Week: T-Nuts
That thingie mounted onto the back of the (perfectly good) Vivitar 285 at left is called a "T-nut." They are pretty easy to find in 1/4x20 or 3/8" sizes. It is fastened with "JB Weld" glue.
Long story short, anything you can stick a T-nut to can be mounted on a light stand. In fact, you could purposely destroy the hot shoe of a flash without a PC jack to get access to the synch wires and easily fashion your own pigtail 1/8" synch cord, using the T-nut to mount the flash. But that's another post.
You can also get spiked t-nuts that would mount to the underside of a small piece of wood (which would increase the surface area for the gluing) if you are concerned about strength of the bond.
Added bennie: The t-nut mount gets the flash head very close to the axis of the umbrella shaft, if you are softening your light that way.
(Thanks or the heads-up, Chad!)
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