That's not a kickdown cable. That's a Throttle Valve cable, it's far more complex in its function than any old school kickdown cable was. It controls the hydraulic pressures inside the transmission so you cant just leave it off. If you had actually driven it around like that you'd ruin the transmission very quickly.
And if you dont get the geometry right with the throttle linkages then you'll still burn up your trans. They make adapter brackets to replicate the stock geometry. A certain amount of throttle input has to have a certain amount of pressure inside the transmission so that it knows when and how hard to shift.
Take the time and do this right.
This is a sad picture, but this is how I had mine set up. Since I was able to adjust where the TV cable was fairly easily, I was going to try and do without that adapter bracket I was mentioning, but most people here will tell you that's a bad idea, I had still planned on ordering it. For obvious reasons I never got around to it. By the time I had this motor rebuilt I had a T56, but this is roughly how it needs to be done.