Pull the top plate off of the shifter. The top pawl will likely fall out, as it did here. Clean and lube as you did on the other pawl. You can take the bottom one off if you want, but I usually just blast it and lube it.
Put the pawls back on (the "hooks" should both be on the same side), re-install the e-clip and put the top plate back on. Re-attach the shifter to the brake lever body and try shifting. If everything seems to work, put the cover back on, screw in the barrel adjuster, and reinstall the shifter on the bike.