Engine - Coil

I am trying to model the coil that goes inside the pull string starter for an engine
what would be the best way to model the coil and also to have it working within the pull string encased compartment...

I don't know if this is even possible to have it working within the encased compartment?

I have included a picture for better understanding what I am trying to model

Thank you in advance for any help relating to this question.
:)