Was this some kind of generator motor before? It doesn't look like it used to have an adjustable throttle.
The motorsports engines had what they can an RV throttle control plate. Makes hooking the cable up very simple. Maybe you can find one on ebay or a lawn parts site. It would be easier to spend the $20 or whatever than trying to fab something up with that weird setup.
No, you would have to find a model/serial off of a powersport series motor and try to order the throttle plate assy and the springs from a mower shop or parts site.