I had the same problem with my GL500 Interstate.
Take both hands off the bars and it would start wagging the front wheel. I didn't let it go for only a second or two for fear of a tank slapper.
I had brand new Dunlop tires on.
I asked about it here and got little feedback. Other people have experienced the same thing. I asked about the wobble going away after putting in up graded tapered head bearings. The answer was no.
My solution, don't take both your hands off the bars.
Larry