I spent a while looking at your pictures - you have an automatic transmission (Ford-o-Matic?) - and the bracket on the LH rear of the intake manifold is rigged to operate the "kickdown rod" that drops to the transmission.
This diagram shows how the t-bird levers work - and you have some very similar stuff. You are missing a spring off the kickdown - it holds a pin down at the bottom of the kickdown slot until the carb hits full throttle. You will need this tension spring at some point but not now.
There is a hole that "times" the levers - where you see the Philips screw driver stuck in there. With that part of the linkage locked - and the carb in place (at idle position) - the last rod can be adjusted to fit exactly from the locked linkage to the carb lever. As you can see - that rod has to be bent a good bit to fit around the side of the carb. I believe that was your inital problem?
The linkage rotates counterclockwise (seen from the drivers side) as you push down the foot pedal in the cab. The pedal is attached through a "bellcrank" (firewall pivot) to the linkage on the engine with another adjustable link (it moves upward as the pedal goes down) - and it needs to hold the pedal far enough off the floor to allow some serious amount of travel. As you "floor the pedal" - the linkage takes the carb to full throttle (and the carb's lever stops) - but the link keeps moving in the slot to move the kickdown rod - that then shifts the transmission.
All of this stuff is balanced by springs - and when you put in a "new" part - like a different carb with a different (stiffer) return spring - things get hairy. I put a positve stop on the back of my engine so that I could set the foot pedal height against the return spring - then adjust the carb to the screwdriver stop - and finally adjust the last link (from the firewall to the manifold linkage) to join the two. I think I see enough in the pictures for you to get this part to work - but you are missing the kickdown spring. Don't sweat it for now - put a bolt and heavy washer through the slot - you can see it in this last picture - and you can drive the truck home.