Seasonal jobs that might turn permanent - any advice?

A staffing agency says some roles convert to permanent after 13 weeks. I am in Toledo, in case local advice matters. I would like to avoid a gap in my résumé. Has anyone been converted to permanent?

Thanks for writing this out. I went through something close to it 11 months ago, and it settled down once I kept a simple log of every call and form.

Ask early about permanent openings. Some teams fill them from their seasonal list.