Could be what the shops here call"bump steer" Its when your front suspension is getting a littled tired or new springs are too hard.
The horizontal bit is the steering damper.
Mine gets a wobble in the steering at about 80kph when I turn the wheel about 10 degrees.
'Gets worse towing with some weight on the rear and its lifting the front a little
ARB suggested that is a damper problem but it needs more investigation although everything is good or newish ,had a wheel alignment and new tierods a few months back and the wheels are balanced.
The damper is the only old part left.
Every company that makes a shock absorber foR a cruiser makes a damper so there must be 15-20 choices.
Im using these shocks and was going to try their damper.
My shocks are canadian so you maybe able to get their products cheaper under another name if you needed a damper.
http://www.raw4x4.com.au/mainmenu.html
Does anyone know basic test for a damper when its removed? I was thinking its like a shock that gets a soft spot?