In English, "dawn" only occurs in the morning, so when used metaphorically it always refers to the advent of a thing. The word you're looking for is "twilight", which when used metaphorically means the end or decline of a thing. Thus Nietzsche's Götzen-Dämmerung is translated Twilight of the Idols.
There's also the word "dusk", which is the opposite of "dawn", but it tends not to be used metaphorically.
He relocated to Florida towards the end of his life.
*edited the part where I assert OP was wrong.