Unemployment - Private Health Insurance

Hello, I am preparing to apply for an EEA4 as my spouse is husband. He was unemployed for period of <4 months earlier this year. I have been told that should provide 1) proof of private medical insurance and 2) show that he was actively seeking work. For the latter, what does this entail? He did not register at a Job Centre. He was registered for the second half of this time at an outplacement centre (provided by his former employer). He was actively seeking work but this correspondence was not via email for the most part so I've limited email trail. (I can reconfirm this.) I can provide bank statements showing we could cover our costs. And we had private insurance all for the last month. As lucks turns out, I can go back and pay for this last month. Should I do this? Would this plus: 1) the banks statements; 2) a limited trial of emails 3) confirmation of his registration at the outplacement centre suffice? Or can I forgo getting the last mo of private health insurance. Best