‘senility’ does not mean ‘extreme old age when a man behaves like a fool’
‘Senility’ is an age-related condition of cognitive decline. It doesn’t require extreme old age and it doesn’t imply ‘behaving like a fool’.
I can’t think of any single word having such a meaning. Expressions like ‘old fool’ or ‘old coot’ describe the person well-enough but not the time period. It often refers to people making poor choices out of stubbornness, and is not usually associated with senility.