727 won't shift to third

I agree that you shouldn't drive it without the kickdown hooked up or you may burn up the trans. They may have the kickdown lever wired solid on the trans. since it's not hooked up and that's why it isn't shifting right. Since you don't have any linkage your best bet is to buy a Lokar kit and install it. Much better looking and functioning than the stock stuff.

Just thought I'd add it'll take you longer to fab anything that'll work as (it's pretty picky on getting it right) than install a Lokar kit and the Lokar kit will probably cost less than stock used stuff.