Explaining a gap after caregiving or layoff after 13 years as a production planner

My résumé shows a gap from a layoff and some health issues. I have done some volunteering and a course during that time. What do you say in interviews?

I listed the volunteering and course under the same dates and kept the explanation to a sentence in the cover letter.

A short, honest line such as 'family caregiving' is enough for most employers. They mostly want to know you are ready now.