I think I understand HOW Javascript has to work in order to be O.K. for section 508. But I have been unable to find an answer to a related question: does my site need to work W
Section 508 compliance rules do not specify at all whether you use or do not use Javascript. It merely enforces the fact that you must provide equal access to the information you are presenting electronically, regardless of electronic delivery method. For a website, whether that is done by making your website accessible (with or without javascript), a text-only version of your entire website, or a phone number that someone can call that is staffed appropriately and has access to all that information, you have satisfied the intent of the law.
One of the best resources for information on 508 compliance is http://www.section508.gov.