Increasingly the employment gap doesn’t matter and a lot of employers advise interviewers to not ask. Often the answer is something like care taking, illness, or other semi-protected life event that HR just doesn’t want to unwrap.

I would be honest. There’s no better excuse for not working than you were unable to due to an illness. As mortals we all appreciate this reason. If you are interviewing with someone who doesn’t understand that, do you really want to work for them?

If it’s the nature of the illness that you are uncomfortable disclosing be aware you are entitled to medical privacy. Just tell them it was a serious illness that prevented you from working and if they ask for specifics tell them it is private. Again if they can’t respect that 1) they may be violating local or state laws if not their own policies, 2) do you want to work for them?