1967 Ford Ranchero stalls when medium to hard braking

This the second time i will be asking the same question. 1967 ford ranchero, 289 cu. in., C-4 auto trans and power brakes-factory disc in front drums in the rear. I asked this question of the pros but I got a very general answer which does not help. The tune up is good, vacuum advance: works properly, fuel filter is clean, breaker points have been replaced and work perfectly, no severe vacuum leaks. every suggestion the Pros made has been checked with no problems indicated. The Problem: The car stalls under medium to hard braking and also when at a stand still, in gear, I goose the car letting on the accellerator immediately, the car stalls. I have owned thios car for 18 years and this issue has been a problem all those years. I am not ASE certified but I do know this car quite well.
I remember something about a devise that was located on the throttle linkage and it's purpose was to counter-act this very problem. I hope one of you, "been around for ever", car guys have some serious answers. Thanks for your time, Rif-Raf