Does anyone know if there is a small ITR like reel that is max 1.5cm (0.6 Inch) long and 1cm (0.4 Inch) thick?

I have never seen one. You can check with James George, the inventor. If you have Facebook you can find him there.

How long does the "action" have to be?

Perhaps a reel isn't the optimal solution.

Or, you might be able to perform the vanish or effect through a different hookup or by using a different gimmick. (Think pull or holdout.)

Rats, I missed the '30 minute limit' for editing my post...

You might be able to enhance the end effect by using a different gimmick, rather than a reel. (Everything from an animation to even a vanish or transformation.)

There are lots of ways to get 'mechanical traction' other than a reel.

Good luck!