Heh... even better:
[Edit:swapped out for an even better version...]
Grab a 1-2" long cylindrical piece of balloon (or a piece of - ahem - textured translucent rubbery material which conveniently comes in tubular shapes of about the right width. *). Now, make two *sturdy* square cradstock frames (may want to use matboard for this, or reinforce with popsicle sticks), with a circle cut out of the middle. These will be the "doorframe" for the sphincter. Now insert one of these frames squarely into one end of the tubular piece of rubber, then thread the rest of the tube through the center of both frames, and loop it over the second frame. You should now have a short cylindrical rubber tunnel, framed by two square pieces. loop a string around the middle of the tunnel. Now pull on the string from opposite end, and the rubber sphincter should close.
You can install the two frames a little distance from each other so you keep a bit of a tunnel effect, or you can sandwich them together (make sure the string can still move freely though) for a more compact sphincter "door". Paint according to your own inspiration. (May need to experiment a bit to get a paint which sticks yet is elastic enough to move with the rubber.)
To paraphrase a famous computer guru: Caution - I have merely proven that this works, I haven't actually tried it yet!
* Just occurs to me that you could use the same type of material to coat the inside corridors with. Get the fancy ribbed kind, non-lubricated.
