1967 Ford Ranchero car stalls under medium to hard braking

Which engine? Things to check tune up? Fuel filter, carb float and or carb power valve(accel pump), Distributor vacuum advance, especially if backfire occurs, Bad point setting, severe vacuum leaks. Any sign of power loss, or pinging under hard acceleration?

289 cu. in., C-4 trans and power brakes: factory disc up front and drums in the rear. All of your suggestions have been checked an all are working fine, no problems indicated. This problem has been with this car from the day I purchased it, 18 years ago. I Seem to remember a device which had as it's sole purpose counter-acting this very issue. It was installed on the accelerator linkage, but my memory is not what it used to be. This problem sure acts like it is 'vacuum' in nature. Rif-Raf

You may have a vacuum leak, get a can of spray gumout, spray the vac lines and maniflod area, when the idle changes, youve found the leak! You want the engine running and spray on the outside but do direct the stream onto the hoses, if it is a vacuum leak, the engine idle will change speed, then you have detected a leak, repair the vacuum leak and see how it runs! Are you talking about the TV cable that runs from the transmission to the throttle linkage? That only comes into play to downshift under hard acceleration from 3rd to 2nd gear. The other part is an anti stall dashpot for deceleration...

The other thing you might want to try is setting the mixture, it might be a wee bit lean and starving for fuel.
Use a tach gauge, set rpm to lowest setting possible while idling, then adjust each screw for maximum rpm. Then reset the idle to proper spec.