The linkage you have shown there is the same as mine used to be, well more or less.
It runs as a flexible cable from your accelerator pedal to the carb, then that rod linkage down to the diverter plate in the exhaust manifold. Its there for quicker warm ups by blasting hot gasses onto the bottom of the inlet manifold.
Which auto box have you got? (TH400 or the Torqueflite).
The TH400 has a kickdown solenoid operated by a slide switch above the throttle pedal, dont know about the Torqueflite Im afraid.
However when I had similar problems they were all carb related, worn jets and air leaks.
Good luck!