Transmission kick down cable problem

The cable should push IN when the gas pedal is pressed. I've seen this reversed on adapted carburetors, kind of hard to do with all stock linkage. Mid 60s TSMs state that the initial adjustment should be done with the linkage in idle position (pedal not pressed). Make sure the choke isn't set -- it should not be in a fast-idle position. Adjust the clevis on the cable to a "loose pin pit" -- the pin holding it to the carb linkage should easily slide in and out. Then adjust the cable two full turns long. That gives you a starting point. From there, lengthening the cable will increase pressure in the trans and make for slightly faster, firmer shifts. In my experience you can't really go more than about two full turns longer, with 1 to 1.5 preferred. At two full turns the trans will prematurely down-shift going up some hills as you press the gas pedal to hold speed. The cable acts as a kick-down as well as controlling internal pressure. If you are under 55-60 mph or so and the cable "bottoms out" the trans will kick-down to second gear. You might have the gas pedal down far enough pulling a short steep hill but not really want/need to kick down. I ran mine at 3.5 turns after loose pin all the time. That was in a 63 American with a slightly hopped up 195.6 OHV and 3.31 rear gears. A big car might not "like" 3.5 turns total, as it takes more throttle to hold speed (heavier car).

Later 60s and early 70s TSMs just give a pressure reading. The "two turns after loose pin fit" seems to work well even on later cars.

It's important that the cable moves freely. Hold the clevis between your thumb and one finger. You should be able to push it in and pull it out easily. If it takes more to hold and move it than that the cable isn't free enough. There is a light spring in the transmission on the valve, but I don't think it's enough to push the cable out once it's pushed in, not by itself. It's there to "help" the throttle linkage, that's all... IIRC.

If the cable isn't easy to move it must be removed. You can then coil the cable and soak it in penetrating oil in the bottom of a bucket. The outer plastic covering may come off, but that's not an issue (actually a help later!). I use a 50/50 mix of ATF and acetone, with the bucket covered (a lid is preferred, but a towel will slow evaporation of the acetone). I usually soak it overnight, then remove, dry, and work the cable to make sure it's free. May take another soaking (add a little acetone as it evaporates easily) and working to free up entirely. Once it's free dry it off and reinstall. With the plastic covering gone spraying it once or twice a year with penetrating oil will keep it free.  The oil will penetrate between the coils of the wire covering, something it can't do with the plastic outer shell.