Question about getting medical card in Florida for part-time / seasonal resident

I've already started living part time in Florida in that I've spent something like 6 of the last 11 weeks there but I go back and forth to another state to see family still so I'm currently splitting time essentially between two states. I'm planning next to go out for 2 months and rent a furnished apartment there for this time period, I'm not in a financial position where I can just rent a place long-term and have it sit empty while I'm gone, my understanding is that when I get there next I would need to wait 31 days to be able to show them my rental agreement to get the temporary medical card but are they going to care that it's only a 2 month lease?

I am not sure if they would give me a chance to explain that I'm planning to come back again even after that just that I rarely stay more than 2 months at one time in Florida before returning to my other state for at least a month. I saw also an option is to show mail received from the government but I'm not really sure I understand what kind of mail a part-time resident would have from a government.

Thanks for any advice, this has really been stressing me out.