Steering feels very loose without it. I really notice going over bumps, railroad tracks or anything else that will cause a bit of a bounce. It seems to allow a slight side to side wobble from front tire to back tire. Almost like purposefully wiggling the handle bars. The scary part is a quick change in speed or turn.. Example: Passing and quickly jumping back into your lane but braking to get between cars. This causes a whole lot of front to rear wobble. I don't like it. I can even feel a little wobble just barely releasing throttle in a turn.
Sounds more like a bike or riding style issue and less like a steering dampner issue. The front to rear wobble sounds like suspension pogoing rather than headshake. But I might just be reading it wrong. The real red flags are the going over bumps/railroad tracks (I'm assuming you're taking those slowly), the wobble under braking (this would put more weight on the front end, exactly the opposite of what causes headshake), the "loose" steering , and releasing throttle in a turn(same as hitting brakes, this would put more weight to the front). None of those are cured by a steering dampner. Some are masked by one though.
Sounds like your grip is too tight, you suspension may be incorrectly adjusted, and you may need to adjust your posture.
If you're hell bent on your dampner, I've seen them mounted underneath the yoke and behind the forks, or (this didn't look like a good idea) mounted on the side from the frame to the fork. I've seen it done, and the guy said it worked. What about behind/below your light, attached to the front of the neck with a decent tab?
Some ideas:
http://www.riderforums.com/ninja-650r-accessories/41771-custom-mod-1-steering-damper.html
http://www.riderforums.com/ninja-65...lled-penske-shock-ohlins-steering-damper.html
These are both on 650's. (1) they have no steering dampners so guys had to get creative putting them on (2) I'm familiar with them, lol.