Brain damage shouldn't happen if you're practicing, because you always have control when you practice. Never anchor the rope to anything when you are practicing and you will be fine. You also have to keep in mind every method has a failure rate, partial is nothing special, so it's just overcoming the fear of failure really.
The best way to overcome the fear of failure is preparedness. You're scared because you think you might fuck it up. So make sure you don't mess up, do everything in your power to ensure that you know what you're doing and you've done everything you could. It will take time. It took me 6+ months to figure out partial and get over my personal fears regarding ctb. You just have to keep trying your best. Hanging is somewhat more reliable than other methods like jumping or using a gun, so you're not in the worst of hands (provided you don't get caught).
I personally was never afraid of getting brain damage, and this is coming from someone who actually got brain damage lol. (not from partial but some other method I used, nothing severe). Maybe when I was younger I was a little worried, but then I exposed myself to videos of people who ctbed so much that I just figured, "They overcame the pain and fear that comes with this. I can do it too." I don't recommend that though as it can be a bit traumatizing for some people, I'm sure you can find other ways.