That is very helpful context. Truly accurate ones don't exist yet, even when they're used in evaluations they require expert interpretation to distinguish behaviors that are motivated by autism from similar ones that can have different sources. They also can have phrasing that confuses autistic people and causes them to give different answers than someone else with the same preferences.
But for convincing your parents, any one that is well-respected or makes a professional-looking results page should help, depending on their priorities and what generally seems most important to them. As Hokulea mentions, the AQ is standard and would likely be a part of the actual evaluation.
In the results page for that link, it says clearly your score, the threshold to recommend an evaluation, and if you've met it or not. It looks like a wide range from 33-50, but the threshold is fairly strict. If you meet it, you are likely to either have autism or symptoms of confounding trauma/personality disorder. My current responses put me at only 35, but the evaluator showed no doubt in my diagnosis. If your parents are convinced by that sort of simple and professionally-acknowledged tool and not likely to dismiss a score that is too close to the threshold, this one could be good.
The other link is good if they could use some more detail or like to see things explained. It does offer a PDF download. To me the look of it more resembles a personality quiz, so it doesn't come off as professional, but it has a lot more information and includes both a paragraph description of the main autistic characteristic it identified, and a list of the top things you agreed with that indicate it.
I think if you had both of them, it would be the most convincing.
A main reason it is harder to diagnose in females is because they tend to be more encouraged and educated on how to consciously use social skills to fit in. A parent might police their daughter's tone over something that they would have found basically acceptable in a son of her age, so he does not get the lesson of which tone is ideal for this situation.
I assume you want the evaluation because there are things you've identified as fitting you already- this information is important as well. They will consider how these symptoms are impacting your life in key areas of social functioning and repetitive behavior, and whether or not it can be explained by anything else. For your parents, it probably matters why you need the diagnosis: As you are still young, and in the US, you could likely get resources for some of the issues you are having. If you can establish the practical gain and ways it will assist you in growing up to be more independent, it may help them understand why it would be worth the time and effort and align with their goals.
If you have any other questions about other details, definitely ask. I'm sure someone can help you figure out the answers.