Doug,
The tumbler unit can be removed from the handle assembly once it's removed from the door. Once you've removed it the entire tumbler unit and key can be dunked into a cleaning solvent to remove all the accumulated gunk. Work the key around as you swish the tumbler around in the solvent. I did this recently to my door lock and have done it to my ignition lock and both of them work fine now. After celaning, I shot s small amount of graphite into the tumblers.
Additionally, you probably should have a new key made, once the lock is cleaned, as the keys get so worn that they often don't work.
This method is a lot cheaper than the new stuff,
Ben
www.reproduce100s.com