I finally figured out an answer to a question I posed more than two weeks ago. It's the only answer. Should I accept it? That is, is it good etiquette for a person to accept an own-answer?
Yes, if you believe that your solution is the best one of all solutions, it should be the one you accept. (However if you based it on one or more answer given by others, or it's not significantly different from existing answers, you can simply describe it in an edit to the question.)
On StackExchange sites we try to make questions and answers useful for future visitors as well as the original poster. Let this be one of your guiding principles when posting here.