I was thinking, since the 140S and the 680S manuals are the same... they were probably produced concurrently and share just about everything.? Also, I believe the TS-680S is a TS-140S but with the addition of 6M. But don't quote me on it.?
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Wouldn't hurt to ask the seller to take a picture of the particular knob from a few angles.
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Anyway, blow up the 2nd image in the ebay item I most recently sent you. Doesn't it look like it is suspended a bit above the plastic compared to the knob to it's right, thereby having a bit of a shaft extension beyond the skirt of the knob?
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Conceptually, if all else fails, if you found a knob that did fit a 1/2 shaft, you could super glue it's shaft onto another knob's shaft to extend that shaft into the body of the TS-680S.
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A bit of a MacGyver I know.
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73 W7STF Sam