Tough to say without a picture. The exploded view from the link below shows a lever (figure 843) not a "linkage". That's on the left forward part of the throat, left facing the throat. I have a Briggs engine with a similar carb that has a 3 inch lever just below the intake tube (figure 730, the square box which I think was for winter engines). There are lots of variations depending on the service type of the engine. Mine is original to a snowblower.
The linkage you mentioned might have been something special. You could attach a lever there which would be convenient when starting the engine as your going close to pull the rope. If a dash mounted remote knob/cable arrangement is desired you could attach a bent lever with a hole for a universal cable. The original lever (843) is held on by screw 112 so not a big deal to make up a lever to replace the original.
http://www.partsandservice.com/bin/ipl.cgi
The drawing shows a governor control lever (538). That must be for turbo mode.