From what I recall of the drag chutes installed on the Falcon 20, the operation was purely mechanical; pull the handle once to deploy the chute and again to drop it.
Our ex - FedEx Falcons were all so-equipped. We had a Safety Equipment section that used to repack the chutes on the odd occasion that they were deployed.
On one occasion when returning from a particularly wet deployment to Decimomannu in Sardinia, one of our F-20s developed a problem and had to deploy the chute on arrival at BOH. Unfortunately the wet chute had frozen during the transit flight back to the UK and when deployed it left the aircraft as a solid block of ice and failed to deploy properly. Heavy braking was called for as a result and every bit of the 7000 ft runway was needed.
The drag chutes have since been removed from the fleet.
Again, if memory serves correctly, the drag chute installed on the UK F-4 Phantom fleet was also purely mechanical in operation using cables and springs. Given the number of occasions that an aircraft suffered a BLC failure resulting in a very high speed landing, the drag chute and crossed fingers was essential for stopping within the 6000 foot length of most fighter airfields.
Seem to recall reading somewhere that in both the F-20 and F-4 examples the chute could be used for assistance in spin recovery...but I have no reference material for this statement...
pp