The cylinder visible at the intake is not the damper, nor the choke. These are what are known as "variable venturi" carburetors (or "constant depression" if you are British :G) and that cylinder forms the top of the venturi. Chevy never used variable venturis, although ISTR Ford experimented briefly in the late 70s with them (before moving on to EFI).
Basically, the piston rises in response to air flow into the engine, to keep the air velocity through the venturi constant. It also lifts a mixture needle, which is tapered to keep the mixture more-or-less constant as the venturi size increases.
The 'damper' goes in the middle of the air piston (that big nut on top of the carb), and slows the movement of the air piston. Serves as roughly the equivalent of an accelerator pump, to compensate for the mixture otherwise going lean as the throttle is opened.
ZS carbs had two different types of 'choke' mechanism, I'm not sure offhand which one would be found on a 69 GT6. One kind is a half-round bar that rotates in front of the venturi and partially blocks it; but the more common type is a valve on the side of the carb that opens additional fuel jets for richer mixture.