If the wobble is that bad perhaps the neck bearings haven't received much attention over the years. Make sure there is grease in there while your at it.

 

Mine used to track true as hell with out hands then it started the handlebar shake after about 3 years (2005 RG) mine turned out to be a slightly warped front brake rotor, bought a set of new floaters and it's back it's old super sable self.

 

Ok I have read the thread about fall away. I tried mine on a jack and the handle bars just fall over and dont return. Guess that means my Steering head bearing has too much play?

 

The neck bearings may be bad. Do you hear a click when you hit a bump? While you have it on the jack, grab your front forks down at the axle and see if you have any play. If they are ok you shouldn't have any movement pulling out on them.

 

no Play when I pull down on the axle. No noises when I go over bumps. I put grease at the zerk fitting and got rid of most of the wheel wobble (Hands Off). Then I did the proceedure to adj the steering head bearing (tighten until starting to get resistance) then back off quarter turn. Ride great now (no wobble)

 

Glad you got it fixed.