Biotin is effective, you have to do many cures. Biotin contains vitamins, especially B8. The biotin is more expensive than brewer's yeast and it makes corn grow. It can be a disadvantage!
You can buy it under many forms: dietary supplement, cream.
Try to detangle the mane and tail everyday and use a hair detangler if needed, it avoid to damage the hairs!
And cut the mane often, so the hairs remain beautiful and healthy.
Shaving the mane will make it regrow thicker and more beautiful. But I agree it is radical!
Brewer's yeast is the most common product used to stimulate the hairs' growth. It is a powder you can add to your horse's ration.
I like castor oil but mix it with olive oil otherwise it sticks a lot. You can apply it directly on the roots of the hairs.
What I also recommend you is to not make hairstyles very often, as they can easily damage the hairs. Don't let your horse with braids more than 12 hours for example.