Pull the cock back to half-cock and put your spring vise on the mainspring tightening the screw til it is snug. Let the cock down and remove the mainspring from the lock. Leave the vise on the spring.
Loosen the sear-spring screw a couple of turns and pop the spring away from the detent in the lockplate, then remove the screw and spring.
Remove the sear screw and the remaining bridle screw. Lift the bridle off the tumbler.
I don't think there is a fly in that tumbler, but check and don't lose it if there is.
Remove the cock screw.
Lay the lock across the jaws of a vise with the jaws gaped to allow clearance for the bridle. A couple blocks of wood will do also.
Use a punch (round) that just fits in the axel-hole of the cock and tap the tumbler out of the cock. The tumbler will fall away from the plate, so provide a means to catch it.
Using your parallel pliars, slightly compress the frizzen spring to relieve the pressure on the frizzen and remove the frizzen screw and frizzen.
Remove the jaw-screw and jaw from the cock and it's tore down 'bout as far as it can be.
Polish any surface that rubs on another including the inside of the lockplate. Be careful when polishing the tumbler shaft and hole that you don't remove too much material, you don't want a sloppy fit. Polish the sear nose and full-cock notch on the tumbler but DON"T change any angles!!! I use a hard arkansas stone for this.
The lock goes back together in reverse order.
