Seasonal jobs that might turn permanent - 5 weeks in

I am looking at seasonal jobs around Tucson that might lead to something longer. There are 13 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 everything in writing and save the confirmation numbers. It made the follow-up calls so much easier.

I was converted after one season because I showed up every day and volunteered for extra shifts. Managers remember that.