The very end of the cable slips over the pin on the throttle plate on the carb...it should be able to pivot easily, but not fall off...hence the little cotter pin in the Jegs kit to retain the cable end...the cable sheath should have a square plastic push style fitting that connects through the bracket....
check the image on this link...it shows the cable end...
https://www.summitracing.com/parts/p..._XYaAnXR8P8HAQ
THis sounds like someone may have put an after market kickdown cable on this...suggest you go back to basics with the bracket kit and anew cable...They are not hard to replace...
