Removing the brake isn't a part of a normal cleaning program. If you're really worried, just spray the brake down with your carbon cleaner of choice and q-tip the brake holes out. The Gas System however, is a different horse all together. You'll be needing a gas drill set with a #15 (.180 dia) & Letter P (.323 dia.) drill for scraping the carbon deposits gas system bores. The best set is available from Sadlak:
If you want, you can make your own with a set of drill bits, some epoxy and 1" oak dowel for handles.