Hi Gord,
This cable controls the air via a mini slide that lives in its own cylindrical bore in the carb body. You can see the brass slide through the slot in the wall of the air chamber. The cable attaches to the air slide using a nipple. The air slide should slide completely out of the carby body by pulling on the cable. If it doesn't come out, try your favourite penetrating oil and perhaps some gentle warming. If it's badly stuck you may be able to give it a little poke through the slot in the side of air chamber.
Go gently: these TT carbs are getting hard to find.
Cheers
Leon