Hello and welcome to Just Answer,
Do you see the part you need in this diagram?
I have seen several Briggs engines. I wanted to be certain that we we talking about the same thing. The white part you are referring to fits into the throttle shaft of the carburetor. The linkage rod fits into the whitre item. The white part is is available only with the throttle shaft. The part number for the throttle shaft is 690024.