I checked into this with a book editor I know and got a really fantastic response :)

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You have an interesting situation here. "For sections" is a prepositional phrase consisting of the preposition "for" and the noun "sections." When a prepositional phrase is used at the beginning of a sentence, it's considered an introductory modifier, which generally signals the need for a comma. Some style guides say that prepositional phrases of four words or less do not require a comma, although I think it's always helpful to clarify the sentence.
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A good way to check if you have a prepositional phrase is to see if you can write the same sentence without a comma by putting the phrases in a different order. "Around dinner time, the cows come home," can also be written as "The cows come home around dinner time." (I have no idea why that's the first prepositional phrase that popped into my head...)
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Anyway, in your case, rewriting the sentence would result in: "Use the following rule for capitalization for sections." This sounds a little awkward, which may be why you got called out on it. Removing the other "for" would help. You could say, "For sections, use the following capitalization rules," or "Use the following capitalization rules for sections."

So, it looks like the comma *can* be there, and adding it can help clarity. But, as she points out in the last paragraph, this can be phrased better. I'll update it with that nice wording.

Thanks!