Seasonal jobs that might turn permanent - 18 weeks in

I am looking at seasonal jobs around Jacksonville that might lead to something longer. This is my first time dealing with any of this. I would like to avoid a gap in my résumé. Is it worth applying to several at once?

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

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