It's the adapter you're using, and sadly thete is little to no support for "dance mode" (which puts the d-pad on the POV hat and allows the whammy to use the left analog) on anything except 32-bit XP or earlier.
I use such an adapter to use my SG with Phase Shift, and I unfortunately have to deal with no whammy. I even tried mapping tilt to whammy in PS, but it was less than usable. You may have better luck than I did trying that with GH3 and WT, unsure.
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