Bob, in my opinion, gutters should only be washed and cleaned. These gutters these days come with a good baked on finish that is intended to last for a long time.
I am always confronted with this question on my residential jobs. I look at the gutters and determine if cleaning will do the job and prefer to do that. Bleach and TSP will usually make them shine.
However, when they become as old as yours, which is on the last leg of life, I would probably suggest that a good cleaning and then painting will improve those gutters tremendously.
It will not hurt a thing and with proper prep work, a good Paint STore paint will adhere nicely.
You will need a couple or even three coats as the paint will show brush marks. Use a good quality brush.
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