That manifold was an early, rudimentary version of today's variable-tuned intake manifold. It's designed to use the principles of ram tuning, where the specific length/volume of a column of air at a particular rpm has a (minor) supercharging effect. The linkage was supposed to tip-in the manifold butterflies to give a short, direct air path at higher rpms.
Maybe the previous owner didn't understand or care about the system, so he ripped it out. Or maybe the car was changed over to earlier carbs that wouldn't accept the system for some reason.