In general, it doesn't really make sense to count someone who isn't trying to be employed as unemployed in general. I am not sure how you would distinguish between a 60 year old who decided they had plenty of money and would rather not work for someone any longer and a 60 year old who got laid off and can't find anyone to hire them for the work they are trained to do.

And, as you say, there are labor force participation numbers if that's what you're interested in.