Ok... these pictures aren't the best, as I took them with my Blackjack II. Hopefully you'll be able to tell what I'm doing, though.
Here's our patient. An old 7 speed Shimano integrated shifter/brake lever.
First, remove this screw.
Then remove the barrel adjuster, and pull the plastic cover off.
Here I've circled the pawls that cause all of the problems.
With a small, pointy object (I'm using a Snap-On straight pick), remove the e-clip on the large pawl.
Here's the straight pick.
You can then slide the pawl down on the stud. If you aren't comfortable removing it completely, you can stop here, like I did. Then spray the hell out of both the pawl and stud with Speed Degreaser, or a similar product. WD-40 is rather weak, and won't do a good enough job. You need an actual solvent. If all else fails, use automotive brake cleaner. Then spray the pawl and stud with lube (I use T9) and re-install the e-clip.
Next, remove this bolt, if you have this type, and remove the shifter from the brake lever body. If not, you will likely have to blast the pawls from the bottom while moving them back and forth with the pick. If you don't have this type, you can stop here and re-assemble. Otherwise, continue on.
Remove this e-clip (if you have it)
You should now have only these parts removed...
(continued due to the 10 image limit....)