Thanks for the link to the video!
I watched it twice and the "clicking" sound may be caused by one of the following:
A) It may be something as simple as the flywheel not being tightened down tightly, allowing for some "play" (looseness) between the flywheel and the shaft.
B) A bent shaft. (Although this one is probably not it.)
C) A loose connecting rod. When you tightened the piston holder (Connecting rod), did you make sure there was no "play" between the connecting rod (piston holder), and the crank shaft?
Also, since it was froze up, did it show any signs of "scratching"? If so, did you hone out (smooth out) the piston cylinder? And finally...
D) The tapping sound you're hearing may be coming from valve lifters. It would be a good idea to check the valve clearance on each of the valves. The proper amount of gap (clearance) can be found on line. The Briggs and Stratton Web site would be a good source for this information.
I hope this is of some help and that I didn't confuse you. :confused2: