If you have the 99 -02 Cougar replace the TPS (throttle positioning sensor) on the throttle body.
if it was electical u would notice gauges fluctuating. cougars have problems with the fuel filters getting clogged which would cause hesitation and in extreme cases stalling
Symptom of bad fuel filter= stalling when slowing down to stop at lights or stop signs.
vacuumm leak
The steering wheel shimmering could be warped front rotors, when slowing down. The stalling when slowing down could be a bad fuel filter.
under the head liner you will have to pull it down to get the motor
the fuse box on a 86 cougar is down beside your emergency brake release. It has a cover, comes off easy
slowing down.
Battle of Stalling Down happened in 1403.
I just put a new battery and alternator in my car, but when i put it in gear or start slowing down to stop..the car die out. Also the brake light is continely on.
its when something is slowing down
go to autozone .com they give free tech help that can be down loaded
Gradually slowing down is 'decelerating'.