the lockset, as it is, is similar to most typical style automotive locks, the "blade/tooth" is utilized as it is more resistant to being "seized" up by corrosion, by nature of the flat plates in lieu of cylindrical "pins"
Being a 2 edged key, brings into place a tie between the sides of the notched key, and all of this is relying on springs, on both edges, to return the "teeth" to a home position. Maybe one of those springs has been displaced, and no longer applies pressure on the tooth, which effectively makes it "hang" out, and twist out of the housing, which I assume you will find when you take it apart, and find that slightly chewed up brass part, again, sitting in the lower bowels of the lock recess.
Now that you found what you found, I'd actually drill the security screws out of the switchlock, take it to a "competent/reliable, and proven" locksmith, and have him disasemble and re-assemble it, replacing any worn springs that tension the teeth. Make sure he has a good key also.
I've disassembled locks like this in the past, and color coded each "tooth" before removing them, so I could insure they actually lined back up correctly with the key (yeah, I goofed a couple times...btdt) but did end up with a functioning lock eventually.. (I had to but junkyard locks, and remove the parts, to get the correct springs I needed)
The tumblers are usually held together with a "lock"strip metal slide in piece, on the side of the tumbler assembly, and can be pulled/pried out to rebuild the set.
I think you did well to find the initial cause, now enlist someone that may be able to really fix it, in a matter of minutes for you, with the assembly in hand..
Locksmiths are hard to find anymore, I have 2 local ones, that have passed the business' down from grandfather, to son, and now grandson... they can do in 5 minutes what it would take me an hour, and make it work.
best of luck.