Seasonal jobs that might turn permanent - first time posting

I am looking at seasonal jobs around Salt Lake City that might lead to something longer. There are 5 people counting on me, so I am trying to be careful. I would like to avoid a gap in my résumé. Which employers treat seasonal workers well?

Keep a list of supervisors' names. A reference from one of them helped me land my next job.

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