As you suspect, the cable that runs down the firewall to the right side of the car is the kickdown or detent cable. Adjustment is made at the bracket just aft of the carb where both the throttle cable and detent cables run thru it. There are 2 types of adjusters. One is a "D" shaped metal tab that is pressed down to release- press it down, when it releases, the center of the housing will move toward the carb under spring pressure. To adjust, move it all the way back, then open the throttle all the way open, push the center housing back as far as it will go, and release the tab.
The other style is adjusted the same way, but the adjuster is unlocked with a screwdriver. On the back side of the bracket, there's a round 1/2" thick plastic ring. The lock is in the top of that and is popped up to release.
Either one can be adjusted in or out to suit how you want it to behave. The detent shift point can be tailored to suit you by making the cable longer or shorter.
***On a 350 or 350C trans, all the cable does is provide some shift feel input (not all) and the detent downshift. The 700-R4 and 200-4R trans will cook if the cable is adjusted like you would a 350.***
