There is a pin to force them shut

The shaft might be sticking from wear or corrosion so sure, fix that, however -

There is a horizontal plastic pin on a lever on the choke side of the primary throttle shaft, this forces the secondary to close if properly adjusted.

Of course, if [ie WHEN] the plastic pin breaks, the secondary can do anything from not close to stick wide open. Been there, done that. I use metal pins now for this function, but anyway that is what pushes the secondary shut.