Here is a simple solution.
Place three stills one after the other in the Timeline; open clapperboard, closed clapperboard, open clapper board, call them One, Two, Three.
Adjust duration to taste, play segment. Voila! Perfect illusion of clapperboard open and closing.
Add sound effect at appropriate moment. Just to try it, I found a free pistol shot sfx, muted it a trifle and it made a satisfying imitation of a clapperboard snapping together.
Notes:
To obtain No. Two, perhaps Ian, who seems to have a cornucopia of clapper board stills, and is typically generous with them, has a duplicate of a closed one.
Or why not draw clapper boards, one open, one closed, and scan them? How hard is that? A black pen and a straight edge and you are in business. That will also leave you free to hand write titles and other effluvia on the boards.
Don't forget to temporarily reduce the opacity of your clapper boards so that you can accurately place them in exactly the same position. Then restore full opacity. Or not. A fadeout may better suit your taste. It will be fun to experiment.
Or, of course, you could instead stack No One on V1, No. Two on V2, and Number Three above that on, surprise, V3 . The duration of all three would have to be the same, and longer, say 8 or 10 seconds, but the fade from One to Two to Three could be managed effectively using the Magic Balls of Opacity.
Totally unnecessary addendum, but I feel like writing:
I used the above method to get Frankenstein's monster to blink in a mock horror movie I am making.
Shouldn't one sound effect be SFK not SFX?
Yes, you could use five stills with the board wide open, partially closed and fully closed and el reverso for the last two. I have not tried it, but if you are a stickler for realism...
You could easily use the system in FCE to record the sound of you slapping two pieces of wood together. Make sure your spouse is out so that she won't stumble upon you doing this.