More than likely..(if it's the original setup) your pedal shaft has worn out the factory bushings and actually worn into the shaft itself. It's hanging up on it's own little groove. This is not uncommon. You need to remove the entire pedal support out from under the dash and fix it.
The support comes out..but it's a pretty good job. you'll need to take the instrument cluster out and push it out of the way. The Pedal support mounts to the firewall at the master cylinder. You'll have to take the brake pedal rod loose, brake like switch, etc...and take it loose at the front of the dash also. After it's totally disconnected, you should be able to tilt the assembly to one side and the work the pedals out. then you can get the support out.
Once its out, you can install a repair bushing kit that the Mustang Supply houses sell..but since you've gone to all this trouble, I'd suggest fixing it one time which will be forever..but installing bearings.
Check out this website:
MustangSteve's Tie Rod Adapters and Lower Ball Joint Adapters for Installation of Granada or Versailles Disc Brakes on 65-73 Mustangs