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What the fork brace actually does is adds torsional strength between the fork tubes.
Where you'll see the effect of this most is actually in high speed cornering.
For a quick demonstration, grab a gyroscope and get it spinning, place it between your fingertips, then try to change it's angle of attack similar to that of leaning your motorcycle wheel over in a turn.
Feel how it pushes your fingertips in different directions as the gyroscope resists changing it's angle? Your front wheel is a big gyroscope and will push your fork tubes different directions when you change it's angle of attack just like the toy tried to do to your fingers. What you'll "feel" on the bike is a washy, weakish almost have to push the bars harder to get the front wheel to respond appropriately feel.
Tie those fork tubes together with a large chunk of metal, and it won't allow the tubes to be pushed different directions, giving you more positive control over the angle of the front tire. When you push lightly on the bars, the tubes will push that tire over faster and easier because there is no longer any flex between the axle and the steering head.
The fork brace will do nothing whatsoever for the famous Goldwing "wobble"...The only thing that will fix that is good tires, properly mounted and balanced, AND properly aligned with the frame, coupled with properly torqued steering head bearings.
As for getting pushed around in crosswinds...that's just a part of motorcycling that we all get used to with additional miles under our belts.