G'day Lee.
It's a plunger, the inner primary is part of the left crankcase.
Yes mugwump, I'm thinking sticky followers or as has been mentioned before, the cam and/or followers have been reground to the point where the followers don't drop far enough to reach the cam.
Anji, have you tried setting the tappets to zero or even a few thou" tight? This should keep the followers firm on the cam base circle and reduce the click. If it doesn't were back to cam/followers.
Cheers