On some 312's (maybe all?), there is an item referred to as Automatic Choke Vent Tube.  It has a special press-in 90° elbow fitting connected to the manifold just below the carburetor (mine is a Carter--don't know if that matters).  From the elbow, the tube travels up to where it is inserted in a grommet in the carburetor body.
It can be seen behind the throttle linkage in the highlighted portion of this photo.

Mine is damaged, but I have not found a parts place or mechanic who is even familiar with this.  Does anyone have a suggestion on where to find or if this part is even needed?  Maybe an idea on how I can fabricate one?  If it helps, this engine is from a 1956 Mercury.