Is it possible to animate on/off of a magnetic mask?

I am not sure if I understand correctly, but if you want to use an effect with a mask, and then later on the same clip without the mask: Blade the clip, and delete the mask in the part where you don't want it. You can also add a short cross dissolve between the two to smoothen the transition.

What is the "effect" you are using?

Could you post a screenshot of the timeline with the Magic Mask to help me visualise precisely what you mean?

Can't you simply drag the effect you want from the effects panel and put it on whatever clip you want. You can use the same effect indefinitely.