What can I, a 13 year old boy, in 8th grade advanced classes, do to prepare myself in a career as a hairstylist?

One thing I would do is understand the industry. The beauty industry is limitless, you an be average or exceptional, both are acceptable and will allow you a career. I have managed and trained hairdressers for 20 years now. It is a fantastic industry. But after you graduate from beauty school, the real work starts. You will want to apprentice and learn much needed skills and techniques for the first 2-3 years after graduating. Study hair heroes of past and current.
Do you want to specialize in cut or color or both? Who inspires you? Do you want to do editorial or run way work? Practice, play, learn.
A great stylist is always learning, understands references.
Start making a look book of inspiration, visuals, styles that inspire you. Think different decades.
The beauty industry is extremely fun, and creative. Aside from skill and having vision, communication and listening is a HUGE part of this industry. Selling yourself, your vision and your skill.
Hope this helps,
Good Luck!

One thing I recommend to people looking at all sorts of different fields is shadowing someone in your field, and I think this could be really fun and useful for you. Shadowing essentially means spending a day (or however long you agree on) with a hair stylist learning about how he/she does his/her job and what the typical day is like. Are you friendly with your hair stylist? Could you ask him/her if you could watch him/her work for a day and learn about his/her job? You could also use that opportunity to ask him/her about the steps necessary to become a hair stylist and other questions you might have.

Learn all you can! 😀

There are educational videos on YouTube of professional stylists that are helpful. Magazines with latest trends, and you may be able to visit a school that offers Cosmetology classes to see the training first.

I also suggest "Job Shadowing" (shadow means to watch closely) work with a stylist for a few days and observe their job! That will be really fun for you!

Stay positive and develop every facet about yourself. You are in advanced classes, stay in advanced classes. Learn as much as you can all the time about the world, beauty, business, health, fitness and etc. Spend some time in different salons and just observe and analyse as much as you can. I think something very important to consider is that you should be a filter not a sponge. Take in all that will be useful and productive and let all the bad stuff go through. It can be a tough career but the $ and flexibility may be well worth it.